transportation zmode selection zroute selection yshortest path yminimum spanning tree...
DESCRIPTION
Mode that minimizes Total Cost zTransportation Cost zInventory Costs ySource yPipeline yDestination - including safety stockTRANSCRIPT
TransportationMode SelectionRoute Selection
Shortest Path Minimum Spanning Tree Transportation Assignment TSP Route Sequencing Tanker Scheduling
Mode SelectionShipRailTruckPlane
Fas ter
Cheaper
More V
ariable
Mode that minimizes Total CostTransportation CostInventory Costs
Source Pipeline Destination - including safety stock
CostsTransportation Cost
Cost per unit UnitsCost per unit
$CWT (based on origin destination freight weight)
$Time (leased dedicated transportation)
InventoryAt the plant
12 ldquocycle quantityrdquoAt the warehouse
12 ldquocycle quantityrdquo Safety stock depends on lead time variability
In the pipeline Annual Volume Days in Transit Days per year
Example (page 187)
Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30
ModeRate
($unit) Time Std Dev in LTShipment
Size (units) TransportPlant
InventoryWarehouse Inventory
Safety Stock Pipeline Total
Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$
Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate
Route SelectionGetting From A to BUnderlying Network
Roads Airports Telecommunication links
Costs of using each linkFind the cheapest (shortest) path
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Mode SelectionShipRailTruckPlane
Fas ter
Cheaper
More V
ariable
Mode that minimizes Total CostTransportation CostInventory Costs
Source Pipeline Destination - including safety stock
CostsTransportation Cost
Cost per unit UnitsCost per unit
$CWT (based on origin destination freight weight)
$Time (leased dedicated transportation)
InventoryAt the plant
12 ldquocycle quantityrdquoAt the warehouse
12 ldquocycle quantityrdquo Safety stock depends on lead time variability
In the pipeline Annual Volume Days in Transit Days per year
Example (page 187)
Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30
ModeRate
($unit) Time Std Dev in LTShipment
Size (units) TransportPlant
InventoryWarehouse Inventory
Safety Stock Pipeline Total
Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$
Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate
Route SelectionGetting From A to BUnderlying Network
Roads Airports Telecommunication links
Costs of using each linkFind the cheapest (shortest) path
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Mode that minimizes Total CostTransportation CostInventory Costs
Source Pipeline Destination - including safety stock
CostsTransportation Cost
Cost per unit UnitsCost per unit
$CWT (based on origin destination freight weight)
$Time (leased dedicated transportation)
InventoryAt the plant
12 ldquocycle quantityrdquoAt the warehouse
12 ldquocycle quantityrdquo Safety stock depends on lead time variability
In the pipeline Annual Volume Days in Transit Days per year
Example (page 187)
Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30
ModeRate
($unit) Time Std Dev in LTShipment
Size (units) TransportPlant
InventoryWarehouse Inventory
Safety Stock Pipeline Total
Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$
Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate
Route SelectionGetting From A to BUnderlying Network
Roads Airports Telecommunication links
Costs of using each linkFind the cheapest (shortest) path
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
CostsTransportation Cost
Cost per unit UnitsCost per unit
$CWT (based on origin destination freight weight)
$Time (leased dedicated transportation)
InventoryAt the plant
12 ldquocycle quantityrdquoAt the warehouse
12 ldquocycle quantityrdquo Safety stock depends on lead time variability
In the pipeline Annual Volume Days in Transit Days per year
Example (page 187)
Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30
ModeRate
($unit) Time Std Dev in LTShipment
Size (units) TransportPlant
InventoryWarehouse Inventory
Safety Stock Pipeline Total
Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$
Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate
Route SelectionGetting From A to BUnderlying Network
Roads Airports Telecommunication links
Costs of using each linkFind the cheapest (shortest) path
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
InventoryAt the plant
12 ldquocycle quantityrdquoAt the warehouse
12 ldquocycle quantityrdquo Safety stock depends on lead time variability
In the pipeline Annual Volume Days in Transit Days per year
Example (page 187)
Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30
ModeRate
($unit) Time Std Dev in LTShipment
Size (units) TransportPlant
InventoryWarehouse Inventory
Safety Stock Pipeline Total
Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$
Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate
Route SelectionGetting From A to BUnderlying Network
Roads Airports Telecommunication links
Costs of using each linkFind the cheapest (shortest) path
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Example (page 187)
Annual Volume 700000 Cost per Unit 3000$ Unit Weight 10 lbs Inventory Carrying 30
ModeRate
($unit) Time Std Dev in LTShipment
Size (units) TransportPlant
InventoryWarehouse Inventory
Safety Stock Pipeline Total
Rail 010$ 21 5 6000 70000$ 27000$ 27000$ 172603$ 362466$ 659068$ Piggyback 015$ 14 2 4000 105000$ 18000$ 18000$ 69041$ 241644$ 451685$ Truck 020$ 5 1 4000 140000$ 18000$ 18000$ 34521$ 86301$ 296822$ Air 075$ 2 02 500 525000$ 2250$ 2250$ 6904$ 34521$ 570925$
Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate
Route SelectionGetting From A to BUnderlying Network
Roads Airports Telecommunication links
Costs of using each linkFind the cheapest (shortest) path
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Multi-Modal SystemsShip from Japan to Long BeachRail from Long Beach to TerminalsTruck from Terminals to DealershipsWhere to change modeHow many channels to operate
Route SelectionGetting From A to BUnderlying Network
Roads Airports Telecommunication links
Costs of using each linkFind the cheapest (shortest) path
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Route SelectionGetting From A to BUnderlying Network
Roads Airports Telecommunication links
Costs of using each linkFind the cheapest (shortest) path
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Example (page 192)
9084 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Shortest Path ModelA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
ApplicabilitySingle OriginSingle DestinationNo requirement to visit intermediate
nodesNo ldquonegative cyclesrdquo
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Tree of Shortest PathsFind shortest paths from Origin to
each nodeSend n-1 units from origin Get 1 unit to each destination
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Shortest Path ProblemA B C D E F G H I J
A - 90 138 348 - - - - - - B 90 - 66 - 84 - - - - - C 138 66 - 156 - 90 - - - - D 348 - 156 - - - 48 - - - E - 84 - - - 120 - - 84 - F - - 90 - 120 - 132 60 - - G - - - 48 - 132 - 48 - 150 H - - - - - 60 48 - 132 126 I - - - - 84 - - 132 - 126 J - - - - - - 150 126 126 -
A B C D E F G H I J Total FromA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total To - - - - - - - - - - Balance - - - - - - - - - -
Net (1) - - - - - - - - 1
A B C D E F G H I J TotalA - - - - - - - - - - - B - - - - - - - - - - - C - - - - - - - - - - - D - - - - - - - - - - - E - - - - - - - - - - - F - - - - - - - - - - - G - - - - - - - - - - - H - - - - - - - - - - - I - - - - - - - - - - - J - - - - - - - - - - -
Total - - - - - - - - - - -
A B C D E F G H I JA - 1 1 1 - - - - - - B 1 - 1 - 1 - - - - - C 1 1 - 1 - 1 - - - - D 1 - 1 - - - 1 - - - E - 1 - - - 1 - - 1 - F - - 1 - 1 - 1 1 - - G - - - 1 - 1 - 1 - 1 H - - - - - 1 1 - 1 1 I - - - - 1 - - 1 - 1 J - - - - - - 1 1 1 -
Distances
Route Chosen
Costs Incurred
Limits
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Minimum Spanning TreeFind the cheapest total cost of edges
required to tie all the nodes together90
84 84
126
15048
348
6613890
120 132
12660
13248
156
AE
D
C
B
J
H
G
F
I
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Greedy AlgorithmConsider links from cheapest to most
expensiveAdd a link if it does not create a
cycle with already chosen linksReject the link if it creates a cycle
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Whatrsquos the difference Shortest Path Problem
Riderrsquos version Consider the number of riders who will
use itSpanning Tree Problem
Builderrsquos version Consider only the cost of construction
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Transportation ProblemSources with limited supplyDestinations with requirementsCost proportional to volumeMultiple sourcing allowedExample Regal Company (Tools)
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
PROTRAC Engine Distribution
500
800 700
500
400
900
200
Belgium
Germany
Netherlands
The Hague
Amsterdam
Antwerp
Nancy
Liege
Tilburg
Leipzig
Miles
100500
500
800
700500
200
400
900
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Transportation CostsTo Destination
From Origin Leipzig Nancy Liege TilburgAmsterdam 120 130 41 62Antwerp 61 40 100 110The Hague 1025 90 122 42
Unit transportation costs from harbors to plants
Minimize the transportation costs involved in
moving the engines from the harbors to the
plants
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
A Transportation ModelPROTRAC Transportation Model
Unit Cost FromTo Leipzig Nancy Liege Tilburg
Amsterdam 1200$ 1300$ 410$ 620$ Antwerp 610$ 400$ 1000$ 1100$ The Hague 1025$ 900$ 1220$ 420$
Shipments FromTo Leipzig Nancy Liege Tilburg Total Available
Amsterdam - - - - - 500Antwerp - - - - - 700The Hague - - - - - 800Total - - - - - Required 400 900 200 500
Total Cost FromTo Leipzig Nancy Liege Tilburg Total
Amsterdam -$ -$ -$ -$ -$ Antwerp -$ -$ -$ -$ -$ The Hague -$ -$ -$ -$ -$ Total -$ -$ -$ -$ -$
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Crossdocking3 plants2 distribution centers2 customersMinimize shipping costs
Direct from plant to customer
Via DC
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
A Network ModelUnit Shipping Costs
Plant to DC DC 1 DC 2
Plant to Customer Customer 1 Customer 2
Plant 1 50$ 50$ Plant 1 200$ 200$ Plant 2 10$ 10$ Plant 2 80$ 150$ Plant 3 10$ 05$ Plant 3 100$ 120$
DC to Customer Customer 1 Customer 2
DC 1 20$ 120$ DC 2 20$ 120$
Shipments
Plant to DC DC 1 DC 2 Total Out
Plant to Customer Customer 1 Customer 2 Total Out
Plant 1 - 180 180 Plant 1 - - - Plant 2 200 100 300 Plant 2 - - - Plant 3 - - - Plant 3 - 100 100
Total In 200 280 Total In - 100
DC to Customer Customer 1 Customer 2 Total Out
DC 1 200 - 200 DC 2 200 80 280
Total In 400 80
Net FlowsNet Flow
Out Supply Net Flow In Demand Net FlowPlant 1 180 200 Customer 1 400 400 DC 1 - Plant 2 300 300 Customer 2 180 180 DC 2 - Plant 3 100 100
Arc Capacities
Plant to Customer Customer 1 Customer 2
Plant to DC DC 1 DC 2
Plant 1 200 200 Plant 1 200 200Plant 2 200 200 Plant 2 200 200Plant 3 200 200 Plant 3 200 200
DC to Customer Customer 1 Customer 2
DC 1 200 200DC 2 200 200
Incurred Costs
Plant to Customer Customer 1 Customer 2 Total Out
Plant to DC DC 1 DC 2 Total Out
Plant 1 -$ -$ -$ Plant 1 -$ 900$ 900$ Plant 2 -$ -$ -$ Plant 2 200$ 100$ 300$ Plant 3 -$ 1200$ 1200$ Plant 3 -$ -$ -$
Total In -$ 1200$ 1200$ Total In 200$ 1000$ 1200$
Transportation Costs ($ 000Ton)
Transportation Capacities (Tons)
Minimum Cost Network Flow Problem
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Good NewsLots of applicationsSimple ModelOptimal Solutions QuicklyIntegral Data Integral Answers
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Bad NewsWhatrsquos Missing
Single Homogenous Product Linear Costs No conversions or losses
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Homogenous Product
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Linear CostsNo Fixed ChargesNo Volume DiscountsNo Economies of Scale
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Integer ModelsCan model nearly everythingSometimes very difficult to solveFoundation in Linear ModelsExpand from there
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
The RulesExactly like Linear Models exceptSome decision variables
restricted to Binary - 0 or 1 Yes or No True or
False Integers
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Steco Warehouse LocationStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
A Linear ModelIgnore leasing for now -- all warehouses
are openObjective Minimize Total CostDecision Variables
Number of trucks from each warehouse to each customer each month
Constraints Enough trucks to each customer Not too many trucks from each warehouse
Recognize this
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Making Discrete DecisionsNew Decision Variables Do we lease warehouse or not -- binary
New Constraints Effective Capacity depends on whether or
not warehouse is open Warehouse A effective capacity is
0 if we do not lease the warehouse200 if we do
This is Linear
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
An Integer ModelStecos Warehouse Location Model
Unit CostsMonthly Lease Unit Cost per Truck to Sales District Monthly Capacity
Warehouse ($) 1 2 3 4 (Trucks)A 7750$ 170$ 40$ 70$ 160$ 200B 4000$ 150$ 195$ 100$ 10$ 250C 5500$ 100$ 240$ 140$ 60$ 300
Decisions YesNo 1 2 3 4
Total Trucks From
Effective Capacity
Lease Warehouse A 0 0 0 0 0 0 0Lease Warehouse B 0 0 0 0 0 0 0Lease Warehouse C 0 0 0 0 0 0 0
Total TrucksTo 0 0 0 0Monthly Demand (Trucks) 100 90 110 60
Lease Cost To 1 To 2 To 3 To 4
Total Truck Cost
Total Cost
Warehouse A -$ -$ -$ -$ -$ -$ -$ Warehouse B -$ -$ -$ -$ -$ -$ -$
Warehouse C -$ -$ -$ -$ -$ -$ -$ Totals -$ -$ -$ -$ -$ -$ -$
Monthly Trucks FromTo
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Special CaseAssignment ProblemSupply at each source 1Requirement at each destination 1Match up suppliers with destinationsHowrsquos this different from single
sourcingAssigning workers to tasks
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
ldquoApplicationrdquoTruckload shippingLoads waiting at customersTrucks sitting at locationsWhich truck should handle which loadNo concern for what to do after thatWhat are ldquosourcesrdquoWhat are ldquodestinationsrdquoWhat are costs
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Traveling Salesman ProblemVehicle at depotCustomers to be served (visited)Vehicle must visit all and return to
depotMinimize travel cost
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
ExampleFull Service BusinessDriver at Service CenterAssigned vending machines to visitWhat order should he visit to
minimize the time to complete the work and get back to the depot
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
ExtensionsIf the ldquocustomersrdquo involve transportation
Customers = truck load shipmentsIf more than one ldquosalesmanrdquo involved
Construct routes for the 7 drivers at the North Metro Service center
If the vehicle has capacity LTL deliveries
If we intersperse pickups and deliveriesIf there are time windows on service
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Basic TSPData issues
Estimate distance by location Calculate point to point distances Calculate point to point costs
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
HeuristicsCluster first Route Second
Build delivery zones with approximately equal work
Route a vehicle in each zoneClustering Approaches
Assign most distant blocks first Sweep Space-filling curve
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Space-Filling CurveEach point (XY) on the mapExpress X = string of 0rsquos and 1rsquos
X = 165 = 1000010 124+023+022+021+020+12-1 +02-2
Express Y = string of 0rsquos and 1rsquos Y = 975 = 0100111 024+123+022+021+120+12-1 +12-2
Space Filling Number - interleave bits (XY) = 10010000011101
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
PropertiesEvery pair (XY) has a unique point
(XY)Every point on the line corresponds
to a single point (XY)If (XY) and (Xrsquo Yrsquo) are close
together (XY) and (XrsquoYrsquo) tend to be close together
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
ClusteringCompute (XY) for each customerSort the customers by their valuesTo build N routes
Give first 1Nth of customers to first route
Give second 1Nth of customers to second route
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
RoutingEach route visits the customers in
order of their values
defines a route on the plane that visits every point We visit the customers in the same order as that route
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Route FirstBuild a single large routeAssign each vehicle a segment of the
route
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Routing HeuristicsSpace-Filling CurveClarke-Wright SavingsNearest NeighborNearest InsertionFarthest Insertion2-interchange
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
2-Interchange
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
2-Interchange
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
2-Interchange
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
2-Interchange
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Route Sequencing
Route Departure Return1 800 10252 930 11453 1400 16534 1131 15215 812 9526 1503 17137 1224 14228 1333 16439 800 1034
10 1056 1425
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
Tanker Scheduling
Trip From Departure To Arrival FromTo Port1 Port21 Port2 0 Refinery3 12 Refinery1 21 162 Port1 8 Refinery1 29 Refinery2 19 153 Port1 32 Refinery2 51 Refinery3 13 124 Port2 49 Refinery3 61
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-
ConsolidationCross dockingMulti-stop shipmentsLarger OrdersDelay shipmentsConsolidate Production
- Transportation
- Mode Selection
- Mode that minimizes Total Cost
- Costs
- Inventory
- Example (page 187)
- Multi-Modal Systems
- Route Selection
- Example (page 192)
- Shortest Path Model
- Applicability
- Tree of Shortest Paths
- Shortest Path Problem
- Minimum Spanning Tree
- Greedy Algorithm
- Whatrsquos the difference
- Transportation Problem
- PROTRAC Engine Distribution
- Transportation Costs
- A Transportation Model
- Crossdocking
- A Network Model
- Good News
- Bad News
- Homogenous Product
- Linear Costs
- Integer Models
- The Rules
- Steco Warehouse Location
- A Linear Model
- Making Discrete Decisions
- An Integer Model
- Special Case
- ldquoApplicationrdquo
- Traveling Salesman Problem
- Example
- Extensions
- Basic TSP
- Heuristics
- Space-Filling Curve
- Properties
- Clustering
- Routing
- Route First
- Routing Heuristics
- 2-Interchange
- Slide 47
- Slide 48
- Slide 49
- Route Sequencing
- Tanker Scheduling
- Consolidation
-