supply chains: distribution, warehousing transportation...

Department of Industrial Engineering

Supply Chains: Distribution, Warehousing Transportation

Jayant Rajgopal, Ph.D., P.E.Department of Industrial EngineeringUniversity of PittsburghPittsburgh, PA 15261



Distribution, Warehousing and Transportation• Distribution: The system used to store and move goods from the

producer/supplier to the customer

• Warehousing: The modes employed to store goods as they move down the supply chain from the producer/supplier to the customer

• Transportation: The specific modes used to move goods in a distribution network

© Jayant Rajgopal, 2016


Distribution systems are major drivers of profitability• E.g., in 2012 spending in this sector was $1.33 trillion

(representing about 8.5% of the GDP)• Can easily exceed 10% of gross revenues (and even higher for

commodity products)• Distribution networks are typically customized to meet a

company’s strategy– Rare to have a “pure” distribution network; most are hybrids of several types

• Example of an outstanding distribution network: Wal‐Mart



Example:

• 135 manufacturing plants in 29 countries• Approx. 15,000 distributors/dealers in 130 countries

– 5 Regional Distribution Centers (Belgium, USA, Uruguay, China and Singapore)

• Local Distribution Centers (Brazil, Mexico, India, etc.)

–Dealerships



Distribution Network Design: Drivers

• Costs (efficiency)– Inventories

– Transportation

– Facilities and handling

– Information

• Customer Service (responsiveness)– Response time– Product variety– Product availability– Customer experience– Time to market– Order visibility– Returnability

vs.



A distribution network should be designed to meet overall supply chain strategy

For an efficient supply chain the network tends to be CONSOLIDATED

• Fewer facilities, with a larger fraction of customer demand being serviced by each facility

• Transportation costs are generally higher• Emphasis on lower system costs



A distribution network should be designed to meet overall supply chain strategy

For a responsive supply chain the network tends to be DECONSOLIDATED• More facilities, each serving smaller regions with fewer

customers • Facility and inventory costs are higher• Emphasis on high responsiveness




Examples

• DECONSOLIDATED

• CONSOLIDATED


Transportation

Total Costs vs. Number of Facilities

Tota

l Cos

ts

Number of Facilities

Inventory costs

Facilities & Handling

Total Costs

Source : Chopra & Meindl: Supply Chain Management



RISK POOLING IN SUPPLY CHAINS: AGGREGATION OF INVENTORY


• How many levels should our supply chain have?

• How many facilities should our supply chain have?

• What volume of demand must each facility service?

There is of course, no single “correct” answer to these questions that applies to all supply chains!


The main benefit of aggregation is that variability is reduced


Demand variability at each of n different locations

Demand variability at one location serving consolidated demand from all n locations


Why is the demand variability lower?

Because the “pluses” and “minuses” at different locations will tend to even out:


LocationDay Std.

Dev.1 2 3 4 5 6 7

1 503 530 542 466 525 437 497 37.58

2 509 488 460 495 514 540 498 24.62

3 486 512 492 540 450 511 521 28.98

TOTAL 1498 1530 1494 1501 1489 1488 1516 15.62


Aggregation lower demand variability lower safety stock levels for the same level of protection against stockouts

• Remember the formula for safety stock: SS = f

Safety stocks depend on the variability of demand (D) – by consolidation we are reducing this variability

• Another way to look at it is that for the same safety inventory, investment we can provide better protection against stockouts



RISK POOLING: ANALYSIS


1…

23

4N

,

,

,

,,

Suppose there are N regions and = mean daily demand in region ; = std. dev. of daily demand in region ;, = order setup and inventory holding costs at warehouse serving location ;= lead-time at location

OPTION 1


RISK POOLING: ANALYSIS


1…

23

4N

,

A centralized warehouse with lead-time LC that handles all demand from all regions, so that it has a demand with mean and standard deviation

OPTION 2


RISK POOLING: ANALYSISAssume the Cycle Service Level (CSL) is specified as 100% (i.e., we require Pr(stockout) )

Option 1: Decentralized warehouses to handle each region, with local inventories. Assume that warehouse has a lead time with mean and standard deviation so that the mean and SD of

lead time demand at warehouse are given by = and = 2 + 2 2

respectively. (NOTE: If the lead time is constant at then =0 and = 2 )

So total safety stock =∑ ∑

2 + 2 2

(or ∑ if the lead time is constant at ).

Total cycle stock = ∑ /2 0.5∑ 2 /



Option 2: One centralized warehouse with aggregated inventories that handles all demand. Note that the aggregate demand from all regions that is now handled by this warehouse is also Normally distributed with

mean ∑ & S.D. ∑ 2∑

NOTE: If demands are independent (i.e., ij=0), then ∑

If we assume that the replenishment lead time at the central location has mean and S.D. , then the lead time demand at the center has mean = and standard deviation

= 2 + 2 2.

(NOTE: Again, if the lead time is constant at then = 2 )

So safety stock here =2 + 2 2

(or if the lead time is constant at )

Cycle stock 0.5 2 /




1…

23

4N

,

,

,

,,

OPTION 1

Total safety stock =∑ 2 + 2 2 &

Total cycle stock=0.5 ∑ 2 /



1…

23

4N

,

OPTION 2

∑ and = ∑ 2∑

Total safety stock 2 + 2 2 & Total cycle stock =0.5 2 /


Inventory Reduction from Risk PoolingSo with aggregation, the reduction in total inventory obtained is

∑ 2 + 2 2 2 + 2 2

+ 0.5∑ 2 / 0.5 2 /

or if lead times are constant at and LC, by

∑ +

0.5 ∑ 2 / 2 /



Inventory Reduction from Risk PoolingConsider the simplest case, where all warehouses have identical costs, all decentralized warehouses service the same amount of demand, and the demands are uncorrelated:

,

• all ij=0 (so that )

Suppose also that …=



Inventory Savings from Risk Pooling∑ + 0.5 ∑ 2 / 2 /

∑ + ∑ 2 / 2 /

∑ ∑ + 0.5 2 / 1/ 1

∑ ∑ + 0.5 2 / 1

(Note that with deconsolidation total safety cycle stock increases by a factor of )



Correlation of demands at different locations also plays a role• Recall that safety stock reduction

= ∑

• All else being the same, if reduces, we get larger reductions in safety stock

• Since ∑ 2∑ it follows that if

ij is negative, then will decrease (and we will save more in safety stocks…)



AN EXAMPLESuppose we have two similar outlets, each with a replenishment lead time of 2 weeks, and we consider consolidating these into a single facility with the same lead time.



Consolidation: Savings in cycle stocksSuppose mean weekly demand at each location is = = =25 units with a S.D. of = =5 units.

Also suppose setup costs are A1=A2=AC=A=$25 per order and holding costs are h1=h2=hC=h=$2 per unit per week.

• If disaggregated: System cycle Stock = 0.5 2 / 0.5 2 / 2 / 2 ∗ 25 ∗ 25/2=25 units

• If aggregated: System Cycle Stock =0.5 2 / 0.5 2 /

0.5 2 ∗ 25 ∗ 50/2 = 17.68units

Note that savings = 25-17.68 = 7.32= 0.5 2 / 2 1


Q1/2 Q2/2

QC/2


Consolidation: Savings in Safety StocksGiven = = 5, and replenishment lead times = =2 weeks

so that = 12 = 252512

Also given, the same 2 week lead time at the consolidated warehouse, i.e., LC=2

Assume we need CSL=0.9 so that zCSL =1.28

• If disaggregated

SS= 1.28 1.28 1.285 2+1.285 2=9.05+9.05

• If aggregated

SS= 1.28 = 1.28 2 1.28 2 505012

Consider the SS for various values of 12…© Jayant Rajgopal, 2016


EXAMPLE


= 5= 5

L= 2 weeks

L1= 2 weeks L2= 2 weeks

Safety Stock = (1.28*

Safety Stock = (1.28*

TOTAL SS = (1.28* 2

5 5 2 ∗ 5 ∗ 5

TOTAL SS = 18.1

= 50= 50

= 100


• If all ij=0, average SS reduces by a factor N, where N is the no. of locations consolidated (Square Root Law)

12 Disaggregated SS=2*(1.28*5*2)

52+52+2∗5∗5∗12 Aggregated SS=1.28* *2

0 18.1 7.1 12.80.2 18.1 7.7 14.00.4 18.1 8.4 15.10.6 18.1 8.9 16.20.8 18.1 9.5 17.21.0 18.1 10.0 18.1

12 Disaggregated SS=2*(1.28*5*2)

52+52+2∗5∗5∗12 Aggregated SS=1.28* *2

0 18.1 7.1 12.8-0.2 18.1 6.3 11.4-0.4 18.1 5.5 9.9-0.6 18.1 4.5 8.1-0.8 18.1 3.2 5.7-1.0 18.1 0.0 0.0



Negative correlation in demands enhances benefits from risk-pooling

• If the demands are negatively correlated reduction in variability is even more pronounced – More chances for “pluses” and “minuses” to even out!

• Variability is lower even if demands at different locations are uncorrelated

• If the demands are positively correlated there is still a reduction in variability but perhaps not as much



Example: Consider a manufacturer of electronic components that distributes its products in the Northeastern U.S.

• Manufacturing facility in Chicago

• Approx. 1500 different products and 10,000 different customers (mostly retailers)

• Two warehouses – one in Boston that serves the New England states, the other in Newark that serves the mid Atlantic region

• Replenishment lead time from Chicago is approx. 1 week at both warehouses

• CEO has specified a Cycle Service Level of 97%

Question: Should the two warehouses be consolidated into a single one in Albany, NY? Lead time will remain at 1 week and we need to maintain the same 97% service.

Shown below is typical demand data (weekly) for two common products: product Y costs $50 and is a slow moving one with a high c.v., while X costs $1 and is a fast moving one with a low c.v. Suppose A′=$20 and i=0.28

Location i Product E(Demand)= SD(Demand)= c.v. = /Boston X

Y100

77.5

50.0750.714

Newark XY

807

36

0.0380.857 © Jayant Rajgopal, 2016


Summary: By consolidating we can “pool” risk


+-

With more demand being handled at a given location the “pluses” and “minuses” in demand will tend to even out. This implies less overall variability. So we have

• reduced overall safety stocks for the same overall fill-rate• equivalently, higher fill-rates for the same total amount of inventory


Aggregation also has other benefits


• Cycle stocks are also generally reduced • Overhead costs tend to be lower (fewer facilities)• Consolidated warehouse gets larger shipments coming in from

the supplier/plant (more demand larger inbound shipments)

– Total no. of orders per year is decreased and we have smaller fixed order processing costs

– Inbound shipments are larger and so transportation costs are usually lower because we can take advantage of economies of scale


However…consolidation also has drawbacks

• Final customers or retailers supplied by the warehouse are farther away

– This increases outbound transportation costs (which are always more expensive than inbound costs to start with, because outbound shipments are more numerous and in smaller quantities)

• Most importantly, responsiveness is greatly reduced because of the increased distances

– This might be unacceptable to a supply chain strategy that is focused first on responsiveness and then on cost.



Management Implications

Consolidation of demand at fewer locations “spreads out” or “pools” risk from variable demand. This means we can• reduce inventory costs (or provide better demand fulfillment

with the same inventory) • reduce facility costs• reduce inbound transportation costs

BUT…• because of increased distances to the customer, consolidation

– decreases responsiveness and

– increases outbound transportation costs© Jayant Rajgopal, 2016


Consolidation is often done selectively: volume, uncertainty, variety and costs determine if a product is a good candidate for consolidation


Centralized Facility Decentralized Facilities

Variety

Uncertainty

Storage costs

Product volume

LowerHigher

Outbound transport costs


Products with high value-to-weight ratios are often good candidates for consolidation

E.g., electronics goods

• Holding costs are usually much higher than shipping costs, so consolidation makes sense

• Cheaper (outbound) transport costs allow for increased responsiveness even with consolidation



Consolidation via Specialization• Consolidate products with a high coefficient of variation (that move slowly and

have high uncertainty) associated with demand

– E.g., Specialty products

• Generally, “fast‐moving” items whose demand can be forecast more accurately are stocked at decentralized locations close to demand – Bricks & Mortar with e‐Commerce (many companies these days) – E.g., Barnes & Noble stores primarily carry “bestsellers” while other books are mostly

sold online– Gap Stores: similar strategy...

• Products that have high warehousing/storage costs

– E.g., controlled environment (temperature, humidity, etc.)

• Products where outbound shipments can also be consolidated into large lots to take advantage of economies of scale and reduce transport costs



Consolidation does not HAVE to be physical – sometimes it could be virtual

• Centralize information and if one location is out of stock, fulfill from another

• Common with many companies, e.g., Wal-Mart, Gap, May Corp.


Information System


Other forms of consolidationProduct Substitution: Using one product to satisfy demand for another – exploits inventory aggregation and helps reduce safety stocks without affecting product availability.

One-way vs. Two-way substitution

Manufacturer-driven

– Dell customer orders a 100-Gb hard drive

– If unavailable, (1) delay/deny or (2) substitute with 120-Gb hard drive (one-way substitution)

– As long as cost differential is small, aggregate demand and carry more of the higher-value component.

Customer-driven

– Customer buys Dean’s milk at Giant Eagle because Giant Eagle brand is unavailable, or vice-versa

– Two-way substitution

– Aggregate safety inventories across both brands

– In general, if customer’s demanded product is out of stock, substitute with another



CONSOLIDATION via COMPONENT COMMONALITY• Exploit consolidation by using the same component/ subassembly in many

products. Very common in the personal computer industry• Without common components

– Demand uncertainty for a component is the demand uncertainty for the product in which it is used

– Need high levels of safety stock

• With common components– Demand for a component is an aggregation of demand for all products in

which it is used– Aggregation reduces demand uncertainty


Model 1A

Model 2B

Model 3C

Model 1A

Model 2A

Model 3A


CONSOLIDATION via POSTPONEMENT

• Delayed product differentiation• Exploit component commonality by consolidating stocks of common components & subassemblies

• E.g., Dell, Benetton• Especially common in products sold over the Internet



Distribution Network ArchitecturesMost distribution networks have some combination of consolidation and deconsolidation in order to address both costs and responsiveness.

The final architecture will depend on many factors:• Company strategy• Facility costs• Product characteristics• Transportation costs• Taxes, tariffs, exchange rates• Political factors• Infrastructure

We will examine some broad architectures next…© Jayant Rajgopal, 2016


Manufacturer Storage with Direct Shipping

Manufacturer

Retailer

Customers

Product Flow

Information Flow



Manufacturer storage with direct shipping (drop‐shipping)

• No retail inventory; orders go directly from customer to manufacturer (e.g., Dell), or customer to retailer to manufacturer (e.g., on‐line retailers like eBags or ShoeBuy.com)

• Best for items that are specialized, high‐value & low‐demand per SKU, with unpredictable demand

• Allows for postponement of customization to the last minute• Costs

• Lower facility & inventory costs but higher transportation costs• Requires a very good information system infrastructure

• Service• Response times are longer• High levels of product variety & availability• Good customer experience• Very rapid time to market• Returns tend to be expensive/cumbersome



In‐TransitMerge NetworkFactories

Retailer

Product FlowInformation Flow

In-Transit Merge by Carrier

Customers



Manufacturer storage with direct shipping and in‐transit merge• Like drop‐shipping but orders to different sources are merged

en‐route so that customer gets a single delivery (e.g., Dell computers with Sony monitors)

• Best for items that are high‐value, with unpredictable demand and possess postponed customization

• Costs• Similar to drop‐shipping but with somewhat higher handling and

somewhat lower transportation costs• Requires a sophisticated information system

• Service• Generally very similar to drop‐shipping but response times might be

slightly more, while customer experience is a little better because a single delivery is received



Distributor Storage with Carrier Delivery

Factories

Customers


Warehouse Storage by Distributor/Retailer



Distributor storage with carrier delivery• Inventory held at intermediate warehouses by retailers/distributors;

Package carriers move items from warehouses to customers • Usually combined with some drop‐shipping (for low volume items)• E.g., Amazon, W.W.Grainger• Best for high‐demand, fast‐moving items• Costs

• Inventory and handling costs are higher than with manufacturer shipping but transportation costs are lower

• Information infrastructure can be simpler• Service

• Response times are better than with manufacturer shipping • Somewhat lower levels of product variety & costs more to increase availability• Time to market not as quick as with manufacturer shipping • Order visibility and returnability are somewhat easier than with manufacturer

shipping



Distributor Storage with Last Mile Delivery

Factories

Customers

Product Flow

Information Flow

Distributor/Retailer Warehouse



Distributor storage with last‐mile delivery• Similar to previous system but instead of package carriers, the

distributor/retailer delivers items from warehouses to customers • E.g., Webvan, Albertson’s (groceries)• Generally requires more warehouses closer to final customer than with

carrier delivery• Best for fast‐moving items for which disaggregation does not lead to too

much extra inventory (e.g., groceries, consumer staples)• Costs

• All costs are generally higher (especially transportation)• Information infrastructure similar to previous system

• Service• Excellent response times – typically, same day delivery• Product variety & availability usually better than with standard retail• Excellent customer experience• Order traceability tends to be quite easy and returnability is usually a non‐issue



Manufacturer or Distributor Storage with Customer Pickup

Factories

Retailer

Pickup Sites


Cross Dock DC

Customer Flow

Customers



Manufacturer or distributor storage with customer pickup• Inventory stored at manufacturer/distributor but customers place orders

by phone or on‐line and travel to designated pickup point to collect their merchandise; orders are shipped from storage site to pickup point if/as required

• E.g., W.W.Grainger, Sam’s Club, Costco• Costs

• Inventory can be kept low with manufacturer or distributor storage• Transportation costs are lower than with other systems that use carriers• Facility costs are low as long as new pickup sites don’t need to be built• Information infrastructure needs to be good

• Service• Very good response times – same day delivery is often feasible• Product variety & availability are similar to other manufacturer/distributor

storage options• Good customer experience• Order traceability tends to be harder and returnability is usually not a big

problem



Retail storage with customer pickup• Most common type of system; inventory stored at retail outlet• Customers walk in or place order over phone before picking up• E.g., Most large retail chains, car dealerships, etc. • Costs

• Inventory costs are higher than with all other options• Transportation costs are lower than with all other options• Facility & handling costs are high• Information infrastructure need not be substantial

• Service• Very good response times• Product variety is much lower & providing high availability is expensive• Highest time to market for new products• Customer experience very case dependent• Order traceability not an issue usually• Returns are easy



Comparative Performance of Delivery Network Designs

Information

Facility & Handling

Transportation

Inventory

Returnability

Order Visibility

CustomerExperience

Product Availability

Product Variety

Response Time

Manufacturer storage with

pickup

Distributor storage with last mile

delivery

Distributor Storage with Package

Carrier Delivery

Manufacturer Storage with In-Transit Merge

Manufacturer Storage with

Direct Shipping

Retail Storage with Customer

Pickup

6 is weakest; 1 is best

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

4

4

4

4

varies

5

5

5

55

5

6

6

5

Source Chopra & Meindl: Supply Chain Management © Jayant Rajgopal, 2016


eBusiness and Distribution• Today every business is an ebusiness!

• The ebusiness side of an enterprise should be viewed w.r.t. responsiveness as well as cost

• What is the impact of online sales on– customer service?– supply chain costs?



Online Sales and Customer Service• Response time

– Physical products vs. Information products• Product Variety

– Netflix vs. your local video store– Amazon vs. Barnes and Noble

• Product Availability• Customer Experience

– access and convenience– customization

• Time to market– Large screen TV sets at WalMart

• Order Visibility & Returnability• Pricing, promotions and revenue management• Efficient funds transfer



Online sales and Costs• Inventory

– Amazon, Dell• Facilities

– Netflix has well under 100 warehouses• Transportation

– lower for products in digital form– Higher outbound costs relative to inbound costs– Large screen TV sets at WalMart

• Information



TransportationFactors affecting decisions - from two perspectives:• Carrier (party that moves or transports the product):

investment & operating decisions based upon– Vehicle-related cost– Fixed operating cost– Trip-related cost

• Shipper (party that requires the movement of the product between two points in the supply chain) aims to balance costs and responsiveness– Transportation cost– Inventory cost– Facility cost

• We will focus only on the shipper’s perspective…© Jayant Rajgopal, 2016


Transportation Modes: U.S. freight value (2007)


Trucks; 71%• Truck Load (TL)• Less-than-truckload (LTL)

Rail; 4%

Water; 1%

Air; 2%

Pipeline; 4%Multimodal; 16%• Truck+Rail, Truck+Water,

Rail+Water, Parcel/USPS/Courier (<150 lbs., Air+Truck),

Other/Unknown; 2%


TL vs. LTL


Truck Load (TL) Less Than Truckload (LTL)• Loads greater than 15,000 lbs.;

typical payload is around 50,000 lbs.; total vehicle weight cannot exceed 80,000 lbs.

• Faster transit times• Trailers typically 48 or 53 ft.• Dedicated shipments• Shipments move point‐to‐point

• Packaging might be provided by carrier

• Flat rate per mile ($2 to $2.50)

• Loads of 100 to 15,000 lbs.

• Slower transit times• Trailers normally 28 or 53 ft.• Intermingled shipments• Shipments move as optimized by

carrier, with multiple reloads• Packaging usually provided by

shipper (e.g., shrink‐wrapped pallets)

• Generally cheaper, but more complex pricing schemes based on weight, distance and other factors


Intermodal: use of more than one mode of transportation to move a shipment to its destination

• Most common example: rail/truck

• Also water/rail/truck or water/truck

• Grown considerably with increased use of containers

• Increased global trade has also increased use of intermodal transportation

• More convenient for shippers (one entity often provides the complete service)

• Key issue involves the exchange of information to facilitate transfer between different transport modes



Package Carriers move time‐critical, relatively small packages via air, truck and rail

• Typically, up to about 150 lbs.• Expensive relative to LTL carriers but provide rapid and

reliable delivery service• Also provide other value‐added services including pickup

and delivery, order tracking, and customization• Preferred mode of transport for e‐businesses• Typically packages are moved to a hub or sorting facility by

TL, rail or air and then delivered in smaller carriers to customers

• Best for high‐value low‐weight items© Jayant Rajgopal, 2016


Design Options for a Transportation Network

• Consider a “buyer” with several locations, who buys from several “suppliers”

• What are the transportation options? Which one to select? On what basis?– Direct shipping network

– Direct shipping with milk runs

– All shipments via central DC

– Shipping via DC using milk runs

– Tailored network



Decisions in Transportation Network Design

• Decisions must obviously consider impacts on transportation costs…

• …but also on– Inventory costs– Facility and processing costs– Coordination costs– Responsiveness

• Typical trade‐offs:– Transportation and inventory costs– Transportation cost and responsiveness to customers



Transportation & Inventory Trade‐off

• Typically, cheaper modes (e.g., ship or TL) have longer lead times and larger minimum shipment quantities, and thus result in higher inventories

• Smaller quantities can often be moved by faster modes (package, air) but are more expensive – preferred for products with high value‐to‐weight ratio

• Choice of final strategy should account for cycle, safety and in‐transit inventory costs (in addition to the transportation costs)



Example (from Chopra & Meindl)

• Appliance maker in Chicago, buys 120,000 motors a year from a supplier in Texas, at $120 per unit. Each motor is shipped 1 day after the order is received.

• Typically bought in lots of 3,000 and each unit weighs 10 lbs. on average. Assume an annual inventory holding rate of 25%

• Shipments by rail take 5 days; trucks take 3 days• Safety stock = 50% of average lead time demand• Golden is also willing to further drop the price to $3/Cwt if batch sizes

are increased to 4,000 • NOTE: 1 Cwt=100 lbs. So 1 Cwt = 10 units.

Carrier Range of Quantity Shipped (Cwt)

Shipping cost ($/Cwt)

AM RailroadNortheast TruckingGolden FreightwaysGolden FreightwaysGolden Freightways

200+ (= 2000+ units)100 (= 1000 units)50-150 (= 500-1500 units)150-50 (= 1500-2500 units)250+ (= 2500+ units)

6.50 ($0.65/unit)7.50 ($0.75/unit)8.00 ($0.80/unit)6.00 ($0.60/unit)4.00 ($0.40/unit)



Example

Lot Size

No. of orderCycles (n)

Cycle Inv.

Safety Inv.

In-Transit Inv.

AnnualInv. Cost

AnnualTransp. Cost

Total Annual Cost

Mode (Q) (120,000 Q)

A

(Q/2)

B C(A+B+C)*120*0.25

n*Transp. Cost per cycle

AM RailAM RailNEGoldenGoldenGoldenGoldenGolden

3,0002,0001,000

5001,5002,5003,0004,000

)1(*365

000,120*5.0

L *120,000365L



Inventory Aggregation• Inventory aggregation results in reduced safety inventory

• While some aggregation can reduce transportation costs, it generally leads to higher costs beyond a point

• Generally, aggregation is good for products with uncertain demand and high value‐to‐weight ratio; e.g., personal computers

• Need to consider tradeoffs between transportation, inventory and facility cost



Example (from Chopra & Meindl)

• Medical device maker in Madison, Wisconsin• Sells directly to doctors and uses 24 DCs around the U.S. to fill orders• DCs are replenished every 4 weeks from Madison using UPS. Lead time

is 1 week and cost is $(0.66+0.26x), where x=lbs. shipped• Two broad products lines:

– HighValue: 0.1 lbs, costs $200. Weekly demand is N(H=2, sH=5); – LowValue: 0.04 lbs, costs $30. Weekly demand is N(L=20, sL=5)– Average customer order is for 1 unit of HighValue and 10 units of

LowValue• Each DC aims to provide Type 1 Service of 99.7%; holding cost is

$0.25/$/year• In addition to current approach, two other options are being

considered• Option A: Maintain current structure but replenish every 1 week• Option B: Eliminate DCs and aggregate all goods in a single warehouse

in Madison; replenish this once a week. Ship orders via FedEx at $(5.53+0.53x)



Example


Current QH=8, QL=80

Option A QH=2, QL=20

Option B

No. of stocking locations NReorder IntervalHighvalue cycle inv. N*(QH/2)Highvalue safety inv. N*(fD,HLTotal Highvalue inv. IHLowvalue cycle inv. N*(QL/2)Lowvalue safety inv. N(fD,LLTotal Lowvalue inv. ILAnnual Inv. Cost (IHcH+ILcL)0.25Shipment typeShipment size (Q)Shipment Weight (W lbs.)Annual Transportation costTotal Annual costs

244 weeks

ReplenishmentHigh+ Low

241 week

ReplenishmentHigh+ Low

11 week

Customer orderHigh + Low


Transportation Costs vs. Responsiveness

• Temporal aggregation: Combining demand over time• This reduces transportation costs but at the cost of reduced responsiveness

• E.g., Steel maker in Cleveland supplies customer orders using an LTL carrier at a cost of $(100+0.01x) where x is the number of pounds of steel on the truck.

• Consider costs over a 12 day period with (1) daily shipments, (2) shipments every 2 days and (3) shipments every 3 days



ExampleDay Demand Daily

ShipmentCost 2-day

ShipmentCost 3-day

ShipmentCost

123456789101112

19,97017,47011,31626,19220,2638,381

25,37739,1712,158

20,63323,37024,100

19,97017,47011,31626,19220,2638,381

25,37739,1712,158

20,63323,37024,100

C.V.=0.48

$299.70$274.70$213.16$361.92$302.63$183.81$353.77$491.71$121.58$306.33$333.70$341.00

$3,584.01

037,440

037,508

028,644

064,548

022,791

047,470

C.V.=0.37

-$474.40

-$475.08

-$386.44

-$745.48

-$327.91

-$574.70

$2,984.01

00

48,75600

54,83600

66,70600

68,103

C.V.=0.16

--

$587.56--

$648.36--

$767.06--

$781.03

$2,784.01


supply chains: distribution, warehousing transportation...

Documents