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Slide #

Matching Supply with Demand:An Introduction to Operations Management

Grard Cachon

ChristianTerwiesch

All slides in this file are copyrighted by Gerard Cachon and Christian

Terwiesch. Any instructor that adopts Matching Supply with

Demand: An Introduction to Operations Managementas a required

text for their course is free to use and modify these slides as desired.

All others must obtain explicit written permission from the authors touse these slides.

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Slide #

The impact of location pooling on inventory

Suppose each territorys expected daily demand is 0.29, the required in-

stock probability is 99.9% and the lead time is 1 day with individualterritories or pooled territories.

Pooling 8 territories reduces expected inventory from 11.7 days-of-demand

down to 3.6.

But pooling has no impact on pipeline inventory.

Number of

territories

pooled

Pooled territory's

expected demand

per day

(a)

S units

(b)

days-of-

demand

(b/a)

units

(c)

days-of-

demand

(c/a)

1 0.29 4 3.4 11.7 0.29 1.0

2 0.58 6 4.8 8.3 0.58 1.0

3 0.87 7 5.3 6.1 0.87 1.0

4 1.16 8 5.7 4.9 1.16 1.0

5 1.45 9 6.1 4.2 1.45 1.0

6 1.74 10 6.5 3.7 1.74 1.0

7 2.03 12 7.9 3.9 2.03 1.08 2.32 13 8.4 3.6 2.32 1.0

Expected inventory Pipeline inventory

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Slide #

Location pooling and the inventory-service tradeoff

curve

Location pooling shifts the

inventory-service tradeoffcurve down and to the right.

For a single product, location

pooling can be used to

decrease inventory while

holding service constant, or

increase service while

holding inventory cost, or a

combination of inventory

reduction and service

increase.

Or location pooling can beused to broaden the product

line.

0

2

4

6

8

10

12

14

16

0.96 0.97 0.98 0.99 1

In-stock probability

Expectedinvento

ry(daysofdemand)

Inventory-service tradeoff curve for different levels of location

pooling. The curves represent, from highest to lowest, individual

territories, two pooled territories, four pooled territories, and

eight pooled territories. Daily demand in each territory is

Poisson with mean 0.29 and the lead time is one day.

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Slide #

Why does location pooling work?

Location pooling reduces

demand uncertainty asmeasured with the

coefficient of variation.

Reduced demand

uncertainty reduces theinventory needed to

achieve a target service

level

But there are declining

marginal returns to risk

pooling!

Most of the benefit

can be captured by

pooling only a few

territories.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0 1 2 3 4 5 6 7 8

Number of territories pooled

Exp

ectedinventor

indaysofdeman

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Coefficientofvariati

The relationship between expected inventory (diamonds) and the

coefficient of variation (squares) as territories are pooled. Daily

demand in each territory is Poisson with mean 0.29 units, the

target in-stock probability is 99% and the lead time is one day.

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Slide #

0

100

200

300

400

500

600

700

800

1 2 3 4 5 6 7 8

Number of distribution centers

0.00

0.50

1.00

1.50

2.00

2.50

Totalexpecte

dinventory

Coefficiento

fvariation

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Slide #

Product poolinguniversal design

ONeill sells two Hammer 3/2 wetsuits that are identical except for the logo

silk screened on the chest.

Instead of having two Hammer 3/2 suits, ONeill could consolidate its

product line into a single Hammer 3/2 suit, i.e., a universal design, which we

will call the Universal Hammer.

Surf Hammer 3/2 logo Dive Hammer 3/2 logo

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Slide #

Demand correlation

Correlation refers to

how one randomvariables outcome

tends to be related to

another random

variables outcome.

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20

Random demand for two products (x-axis isproduct 1, y-axis is product 2). In scenario 1

(upper left graph) the correlation is 0, in scenario

2 (upper right graph) the correlation is -0.9 and in

scenario 3 (the lower graph) the correlation is

0.90. In all scenarios demand is Normally

distributed for each product with mean 10 and

standard deviation 3.

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Slide #

Surf demand

Divedemand

Both have

lef t over suits

D ive s tocks

out, left o ver

surf suits

Both s tock

out

Surf s tocks

out, left ov er

dive suits

Q surf

Q dive

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Slide #

Key driver of product pooling

Product pooling is most

effective if the coefficientof variation of the

Universal product is

lower than the coefficient

of variation (COV) of the

individual products:

COV for Surf and

Dive Hammers =

1181/2192 = 0.37

COV for Universal

Hammer =

1670/6384 = 0.26 Negative correlation in

demand for the individual

products is best for

reducing COV

nCorrelatio1demandpooledofvariationoftCoefficien

2

1

380000

390000

400000

410000

420000

430000

440000

450000

-1 -0.5 0 0.5 1

Correlation

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Coefficientofvariation

Expectedprofi

t

The correlation between surf and dive demand for the Hammer 3/2 and

the expected profit of the universal Hammer wetsuit (decreasing curve)

and the coefficient of variation of total demand (increasing curve)

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Slide #

Consolidated distribution results

Consolidated distribution

reduces retail inventory by more than 50%!

is not as effective at reducing inventory as location pooling

but consolidated distribution keeps inventory near demand,

thereby avoiding additional shipping costs (to customers) and

allowing customers to look and feel the product

reduces inventory even though the total lead time increases from 8 to 9

weeks!

Direct

deliverysupply chain

Centralized

inventorysupply chain Locationpooling

Expected total inventory at the stores 650 300 0

Expected inventory at the DC 0 116 116

Pipeline inventory between

the DC and the stores 0 50 0

Total 650 466 116

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Slide #

0

100

200

300

400500

600

700

800

900

1000

0 10 20 30 40 50 60 70

Standard deviation of weekly demand across all stores

Inventory(units)

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Slide #

200

300

400

500

600

700

1 2 3 4 5 6 7 8

Lead time from supplier (in weeks)

Inventory(units)

f f

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Slide #

Four possible capacity configurations: no flexibility

to total flexibility

The more links in the configuration, the more flexibility constructed

In the 16 link configuration plant 4 is flexible enough to produce 4 productsbut plant 5 has no flexibility (it produces a single product).

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Slide #

How is flexibility used

Flexibility allows production shifts to high selling products to avoid lost sales.

Consider a two plant, two product example and two configurations, no

flexibility and total flexibility:

If demand turns out to be 75 for product A, 115 for product B then..

Product Demand Plant 1 Plant 2 SalesA 75 75 0 75B 115 0 100 100

Total Sales 175Plant Utilization 88%

ProductionWith no flexibility

Product Demand Plant 1 Plant 2 SalesA 75 75 0 75B 115 15 100 115

Total Sales 190Plant Utilization 95%

ProductionWith total flexibility

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Slide #

The value of flexibility

Adding flexibility increases capacity utilization and expected sales:

Note: 20 links can provide nearly the same performance as total flexibility!

800

850

900

950

1000

80 85 90 95 100

Expected capacity utilization, %

Expectedsales,u

nits

No flexibility

Total flexibility

20 links

11 links

12 links

These data are

collected via simulation

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Slide #

Chaining: how to add flexibility

A chain is a group of plants and products connected via links.

Flexibility is most effective if it is added to create long chains.

A configuration with 20 links can produce nearly the results of total flexibility

as long as it constructs one large chain:

Hence, a little bit of flexibility is very useful as long as it is designed correctly

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Slide #

When is flexibility valuable?

Observations:

Flexibility is most valuable

when capacity approximately

equals expected demand.

Flexibility is least valuable

when capacity is very high or

very low. A 20 link (1 chain)

configuration with 1000 units of

capacity produces the same

expected sales as 1250 units

of capacity with no flexibility.

If flexibility is cheap relativeto capacity, add flexibility.

But if flexibility is expensive

relative to capacity, add

capacity.

400

500

600

700

800

900

1000

60 70 80 90 100

Expected capacity utilization, %

Expectedsales,units

No flexibility

20 links, 1chain

C=500

C=750

C=880

C=1000

C=1130C=1250

C=1500

C = total capacity of all ten plants

O t k ith it li

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Slide #

One way to make money with capacity pooling:

contract manufacturing

A fast growing industry:

But one with low margins:

Total revenue of six leading contract manufacturers

by fiscal year: Solectron Corp, Flextronics

International Ltd, Sanmina-SCI, Jabil Circuit Inc,

Celestica Inc and Plexus Corp. (Note, the fiscal

years of these firms vary somewhat, so totalrevenue in a calendar year will be slightly

different.) 0

10000

20000

30000

40000

50000

60000

70000

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

Fiscal year

Revenue(inmillion$

2003 data:

Firm Revenue* Cost of goods* Gross MarginFlextronics 14,530 13,705 5.7%Solectron 11,014 10,432 5.3%Sanmina-SCI 10,361 9,899 4.5%Celestica 6,735 6,474 3.9%Jabil Circuit 4,729 4,294 9.2%Plexus 807 755 6.4%* in millions of $s