shipsmart tm : the model and the computer science
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ShipSmartShipSmartTMTM::The Model and the Computer The Model and the Computer ScienceScience
Jonathan SheffiUniversity of Maryland
College ParkApril 17, 2000
OutlineOutline
The EOQ Model Reliability and Safety Stock Internal Structure of
ShipSmart ShipSmart™ Example Object-Oriented
Programming
Tradeoff: Production Batch vs. InventoryTradeoff: Production Batch vs. Inventorysimilar tosimilar to
Tradeoff: Shipment Size vs. InventoryTradeoff: Shipment Size vs. Inventory
• Production setup costs vs. Inventory carrying Production setup costs vs. Inventory carrying costscosts
• Transportation costs vs. Inventory carrying Transportation costs vs. Inventory carrying costscosts
Lot Size InventoryLot Size Inventory
A simple business:A simple business: • • Order fixed quantity of goods at fixed intervalsOrder fixed quantity of goods at fixed intervals • • Sell at constant rateSell at constant rate
In StockIn Stock
TimeTime
Inventory costs = quantity x timeInventory costs = quantity x time
Economic Order Quantity ModelEconomic Order Quantity Model
Time (days)
Stock (# of items)
A Single Receiving CycleA Single Receiving Cycle
1 2 3 4 5 6 7 8 9 10 11 12 13Time (days)
Stock (# of items)
A Single Receiving CycleA Single Receiving Cycle
1 2 3 4 5 6 7 8 9 10 11 12 13Time (days)
Stock (# of items)
X
A Single Receiving CycleA Single Receiving Cycle
1 2 3 4 5 6 7 8 9 10 11 12 13Time (days)
Stock (# of items)
X
A Single Receiving CycleA Single Receiving Cycle
1 2 3 4 5 6 7 8 9 10 11 12 13Time (days)
Stock (# of items)
X
Y
Smaller (and more frequent) shipments imply lower Smaller (and more frequent) shipments imply lower inventory carrying costsinventory carrying costs
A Single Receiving CycleA Single Receiving Cycle
TradeoTradeoffs:ffs:
Smaller shipments • low inventory costs• high transportation costs
Large shipments • high inventory costs• low transportation costs
In addition:In addition:Inventory cost-in transit
InventoryInventoryCarrying Carrying Costs/UnitCosts/Unit
In-TransitIn-TransitInventoryInventory
Shipment SizeShipment Size
Inventory CostsInventory Costs
Shipment Size
LTL Rate
Actual rate curve
0
2
4
6
8
10
12
14
0 2 4 6 8 10
Formula rate curve
Transportation CostsTransportation Costs
Basic TradeoffsBasic Tradeoffs
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
Logistics Cost Components as aLogistics Cost Components as aFunction of Shipment SizeFunction of Shipment Size
($/item)COSTS
Shipment Size(items/shipment)
Basic TradeoffsBasic Tradeoffs
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
Transportationcosts
Logistics Cost Components as aLogistics Cost Components as aFunction of Shipment SizeFunction of Shipment Size
($/item)COSTS
Shipment Size(items/shipment)
Basic TradeoffsBasic Tradeoffs
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
Transportationcosts
Cycleinventory
costs
Logistics Cost Components as aLogistics Cost Components as aFunction of Shipment SizeFunction of Shipment Size
($/item)COSTS
Shipment Size(items/shipment)
Basic TradeoffsBasic Tradeoffs
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
In-TransitInventory
Transportationcosts
Logistics Cost Components as aLogistics Cost Components as aFunction of Shipment SizeFunction of Shipment Size
($/item)COSTS
Shipment Size(items/shipment)
Cycleinventory
costs
Basic TradeoffsBasic Tradeoffs
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
In-TransitInventory
Transportationcosts
Total inventory
costs
Logistics Cost Components as aLogistics Cost Components as aFunction of Shipment SizeFunction of Shipment Size
($/item)COSTS
Shipment Size(items/shipment)
Cycleinventory
costs
Basic TradeoffsBasic Tradeoffs
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
In-TransitInventory
Total logisticscosts
Transportationcosts
Total inventory
costs
Logistics Cost Components as aLogistics Cost Components as aFunction of Shipment SizeFunction of Shipment Size
($/item)COSTS
Shipment Size(items/shipment)
Cycleinventory
costs
Basic TradeoffsBasic Tradeoffs
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
In-TransitInventory
Total logisticscosts
Transportationcosts
Total inventory
costs
Logistics Cost Components as aLogistics Cost Components as aFunction of Shipment SizeFunction of Shipment Size
Opt. size
($/item)COSTS
Shipment Size(items/shipment)
Cycleinventory
costs
Basic TradeoffsBasic Tradeoffs
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
In-TransitInventory
Total logisticscosts
Transportationcosts
Total inventory
costs
Logistics Cost Components as aLogistics Cost Components as aFunction of Shipment SizeFunction of Shipment Size
Opt. size
($/item)COSTS
Shipment Size(items/shipment)
Least costCycle
inventorycosts
TotalTotal Logistics CostLogistics Cost
Safety Stock CostsSafety Stock CostsIn Transit Inventory CostsIn Transit Inventory Costs
Transportation CostsTransportation CostsCycle Inventory CostsCycle Inventory Costs
Other CostsOther Costs
Elements of Total Logistics Costs
TotalTotalLogisticsLogistics
CostsCosts= 2 * (Cycle Inventory Costs) (Transportation Costs)2 * (Cycle Inventory Costs) (Transportation Costs)
(Demand Rate)(Demand Rate)
In-transitIn-transitInventoryInventory
CostsCosts
SafetySafetyStockStockCostsCosts
OtherOtherCostsCosts
Analytical Expressions
OptimalOptimalShipmentShipment
SizeSize= 2 * (Transportation costs) (Demand rate)2 * (Transportation costs) (Demand rate)
(Cycle Inventory Costs)(Cycle Inventory Costs)
Transit TimesTransit Times
Transit delivery times varyin random fashion.
Each mode and carrier ischaracterized by a distribution
of delivery times.
InventoryInventory
TimeTime
Effect of Shipment DelayEffect of Shipment Delay
Regular on-time delivery
InventoryInventory
TimeTimeDelay
One delivery delayed
Effect of Shipment DelayEffect of Shipment Delay
InventoryInventory
TimeTimeDelay
Delivery pattern with a single delay
Effect of Shipment DelayEffect of Shipment Delay
InventoryInventory
TimeTimeDelay
Erratic delivery pattern
Effect of Shipment DelayEffect of Shipment Delay
Effect of Safety StockEffect of Safety Stock
InventoryInventory
TimeTime
Safety stock level
InventoryInventory
TimeTime
Avoiding stock-out
Effect of Safety StockEffect of Safety Stock
Transit Time
Probability
Transit Time Density FunctionTransit Time Density Function
Transit Time
Probability
Average Time
Transit Time Density FunctionTransit Time Density Function
Transit Time
Probability
95 PercentileAverage Time
Transit Time Density FunctionTransit Time Density Function
Transit Time
Probability
95 PercentileAverage Time
Safety Time
Transit Time Density FunctionTransit Time Density Function
Transit Time
Probability
95 PercentileAverage Time
Safety Time
Safety Stock for 95% Fill Rate =
(Safety Time) x (Sales Rate)
Transit Time Density FunctionTransit Time Density Function
The Internal StructureThe Internal Structure
Calculations are performed for each option separately
In case there is one segment:– Optimal shipment size is calculated
using the EOQ formula– Takes into account minimum
frequency and storage capacity– Calculates all other output values
The Internal StructureThe Internal Structure
For multiple segments:– Rank vehicle capacities– Find how many vehicles are needed for
each segment– Loop over the second largest, third
largest, etc.– Use optimal solution to calculate all
output values (including the segment solutions)
ShipSmart Example ShipSmart Example
Tactics for the Rail Tactics for the Rail OperatorOperator Reduce shipment price Tighten delivery time Tighten reliability Compete for lower valued
commodities Compete for commodities which
ship in high volume
Procedural vs. OOPProcedural vs. OOP Procedural programming:
– Organize system around procedures that operate on data
(do-something <data> <arg> ...) (do-another-thing <data>)
Object-oriented programming:– Organize system around objects that receive messages (<object> 'do-something <arg>) (<object> 'do-another-thing)– An object encapsulates data and operations
Advantages of OOPAdvantages of OOP• Simplicity: software objects model real world objects, so the
complexity is reduced and the program structure is very clear• Modularity: each object forms a separate entity whose internal
workings are decoupled from other parts of the system• Modifiability: it is easy to make minor changes in the data
representation or the procedures in an OO program. Changes in the behavior of an object do not affect any other part of a program, since the only public interface that the external world has to an object is through messages
• Extensibility: adding new features or responding to changing operating environments can be solved by introducing a few new objects and modifying some existing ones
• Maintainability: objects can be maintained separately, making locating and fixing problems easier
• Reusability: objects can be reused in different programs
Elements of OOPElements of OOP
Class: – specifies the common behavior of
entities
Instance:– A particular object or entity of a given
class
Space War Class DiagramSpace War Class DiagramSHIP
position:velocity:num-torps:POSITIONVELOCITYMOVESHIP?ATTACKDISPLAYCLOCK-TICKEXPLODE
PLANETposition:POSITIONPLANET?DISPLAYCLOCK-TICK
TORPEDOposition:velocity:target:proximity-fuse:TORPEDO?POSITIONVELOCITYMOVEDISPLAYCLOCK-TICK
Space War Class DiagramSpace War Class DiagramSHIP
position:velocity:num-torps:POSITIONVELOCITYMOVESHIP?ATTACKDISPLAYCLOCK-TICKEXPLODE
PLANETposition:POSITIONPLANET?DISPLAYCLOCK-TICK
TORPEDOposition:velocity:target:proximity-fuse:TORPEDO?POSITIONVELOCITYMOVEDISPLAYCLOCK-TICK
• Ships and torpedoes have some behavior that is the same – is there are way to capture this commonality?
Space war game with Space war game with InheritanceInheritance MOBILE-THING
position:velocity:MOBILE-THING?POSITIONVELOCITYMOVE
SHIPnum-torps:
SHIP?ATTACKDISPLAYCLOCK-TICKEXPLODE
TORPEDOtarget:proximity-fuse:
TORPEDO?DISPLAYCLOCK-TICK
is-ais-a
SHIP class is a specialization or sub-class of the MOBILE-THING class
– SHIP is-a MOBILE-THING– SHIP inherits the state and behavior
of MOBILE-THING
MOBILE-THING class is a super-class of the SHIP and TORPEDO classes
PLANETposition:POSITIONPLANET?DISPLAYCLOCK-TICK
has-atarget
Any Questions?Any Questions?? ??
??
?
Jon Sheffijsheffi@mit.edu
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