gravier and kelly 20110419

8/6/2019 Gravier and Kelly 20110419

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Measuring the Cost of Complexityin Supply Chains:

Comparison of Weighted Entropyand the Bullwhip Effect Index

Michael J. Gravier, PhD, CTL

Department of Marketing

Brian Kelly, PhDDepartment of Mathematics

Bryant University

Smithfield, Rhode Island, USA


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The Emperors New Suit Fabbe-Costes, N., & Jahre, M. (2008). Supply chain integration and performance:

a review of the evidence. International Journal of Logistics Management, 19(2), 130-

154.

Fabbe-Costes, N., & Jahre, M. (2007). Supply chain integration improvesperformance: The Emperors new suit? International Journal of Physical Distribution

& Logistics Management, 37(10), 835-855.

Major issue: A lot of faith in supply chainintegration, but it raises more questions than itanswers!

A

genda

IntroductionIntroduction Literature Methodology Analysis Conclusion


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R

esearch Thesis Increasingly complex supply chains mean that a

minimum competence at integration is the priceof entry to many industries.

Identifying effective strategies and structuresrequires a global, non-relative measure to makecomparisons.

Purpose:To explore the utility of informationtheorys Shannon entropy as such a measure



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Information as the Core of SCM Supply chain integration

Make or buy decision (how to parse the supply

chain) Alchian and Demsetz, 1972; Magill and Quinzii, 2002

Supply chain risk management

Manuj and Mentzer, 2008



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Supply Chain Integration IdentityCrisis

Defining it:What is it? Are there different kinds ofit?

Measuring it:

How much is needed? What are thereturns to scale?

Countervailing forces:What causes disintegration?Can disintegration be measured?

Costing it:Are resources being used efficiently?



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COMPLEXITY!

Why the identity crisis?

Introduction LiteratureLiterature Methodology Analysis Conclusion


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Complexity Bullwhip Effect

Industrys shift from one factory producingfinished goods to many factories producingcomponents that are eventually assembled into a

more complex good Forrester (1961)

Lee (1997)

Disney and Towill (2003)



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LCD Panel

and

Touchscreen

PCB

Battery

Backplate

Front cover

and speaker

Camera, audio port,

and antenna

Back covers

BlackberryBlackberry

StormStorm

Image from phonewreck.com



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Images from phonewreck.com

Printed Circuit BoardPrinted Circuit Board

(PCB)(PCB)



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How many companies does it take toput together a cell phone?

Around 200!

Best guess from US Census data and industry

sources Only includes up through phone assemblynot

retail sales or subscription services

Levers to reduce or manage complexity(Perona and Miragliotta, 2004)



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Disintegrative Forces

Integrative

Incentives



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Key costs of BlackBerry Storm

Component Cost

Baseband processor $34.82Display module $20.00

Touchscreen overlay $15.50

Camera module $13.15

Memory card $11.50

Memory multichip package $7.50

14-layer PCB $6.20

4-layer PCB $5.38

Lithium ion battery $5.35

RF transceiver $3.13

Other components $64.30

Manufacturing $16.07

Total $202.89

Source:iSuppli



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Key costs of BlackBerry Storm

Component Cost

Baseband processor $34.82

Display module $20.00

Touchscreen overlay $15.50

Camera module $13.15

Memory card $11.50

Memory multichip package $7.50

14-layer PCB $6.20

4-layer PCB $5.38

Lithium ion battery $5.35

RF transceiver $3.13

Other components $64.30

Manufacturing $16.07

Total $202.89

Source:iSuppli

Tantalum



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Causes of Bullwhip Effect

Inefficient supply chain design

Errors in managerial decision-making

The bullwhip effect index (BEI), perhaps mostcommon index of supply chain performence,measures neither of these causes

Steckel et al. 2004



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Shortcomings of BEI

1. Must be calculated at several different levels

Order of aggregation also affects outcomes (Fransoo andWouters, 2000)

2. Not directly comparable across settings in the realworld (Disney and Towill, 2003)

3. BEI doesnt explain cases where information sharingdeteriorates supply chain performance (Steckel, et al.,

2004)

4. Utility for reducing inventory or costs varies widelybased on supply chain strategy and structure (Torres

and Maltz, 2010)



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Shannon Entropy

Lack of studies that compared outcomes of SCstrategies on overall costs and cycle times(Torres and Maltz, 2010)

Integration and supply chain management dependent on information

Shannon Entropy is the amount of additional

information to correct false information

Value of information depends on how much itdecreases uncertainty for the receiver



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Methodology

APIOBPCS Spreadsheet model

Sterman, 2000; Disney and Towill, 2003;Dejonckheere, et al., 2004; Venkateswaran and Son,

2007

Introduction Literature MethodologyMethodology Analysis Conclusion


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Manufacturer

Wholesaler

Retailer

End

Consumer

Distributor

Transportation

Delays



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Step up Demand Scenario


0

1

2

3

4

56

7

8

9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The only demand scenario

for which point of sale

demand information was

unambiguously beneficial

(Steckel et al. 2004)


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Dependent Variables

BEI: ratio of coefficient of variation of ordersplaced to the coefficient of variation of ordersreceived

Shannon entropy without costs for a probabilitydistribution vector P = p1, p2, p3(understocks, overstocks, well stocked):

)ln()ln()ln()3ln(

1)( 332211 ppppppPH

!



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Classic Shannon Entropy

Actually measures extentthat system is prone to

switch states Designed for when

successive strings ofvalues are independently

generated

Ignores costs



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Shannon Entropy (with costs!)

The weighting induces the entropy measure torank in order of decreasing costliness forUnderstocks,Overstocks, and Well stocked.

wou

ou

u

pppp

ppp

pp

!

!

!

2

1

3

1

2

1

3

1

31

3

2

1



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Entropy of Transformed Probabilities

Quantifies intuitivenotions of entropy

Minimized when supplychain preserves efficiency

Maximized when supply

chain performance errorsadd unnecessary cost



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Experimental Design

2 x 2 x 2

4 vs. 3 supply chain levels/echelons

Information sharing vs. no information sharing

No vs. three-week safety stock



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Information

Sharing

Weeks of

Safety Stock

Bullwhip

Index

Cumulative

Entropy

Backlogs Overages Process

Errors

No 3 13.85953 24.88138 17 79 96

Yes 3 7.096962 21.24452 19 55 74

No 0 7.355933 38.21175 82 58 140

Yes 0 3.283364 27.47848 73 30 103

Information

Sharing

Weeks of

Safety Stock

Bullwhip

Index

Cumulative

Entropy

Backlogs Overages Process

Errors

No 3 9.134196 21.42565 11 46 57

Yes 3 6.138986 15.97126 9 33 42

No 0 5.86081235.49958 61 33 94

Yes 0 2.916498 24.04716 50 19 69

Results for4 LevelSupply Chain

Results for3 LevelSupply Chain

Comparing BEI and Entropy

95%increase

17%increase

30%

increase

Introduction Literature Methodology AnalysisAnalysis Conclusion


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4 echelons, 3 week safety stock

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

BullwhipIndex

CumulativeEntropy

InventoryErrors

WeightedAverage

No informationsharing

Informationsharing



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4 echelons, no safety stock

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

BullwhipIndex

CumulativeEntropy

InventoryErrors

WeightedAverage


Informationsharing



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3 echelons, 3 week safety stock

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

BullwhipIndex

CumulativeEntropy

InventoryErrors

WeightedAverage


Informationsharing



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3 echelons, no safety stock

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

BullwhipIndex

CumulativeEntropy

InventoryErrors

WeightedAverage


Informationsharing



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Evolution of BEI (3 week safetystock)

N Inf S r Inf S r

4

Levels

3

Levels

0

2

4

6

8

10

12

14

16

1 4 7 10131619 222528313437404346

0

2

4

6

8

10

12

14

16

1 5 9 13 17 21 25 29 33 37 41 45

0

2

4

6

8

10

12

14

16

1 4 7 10131619222528313437404346

0

2

4

6

8

10

12

14

16

1 5 9 13 17 21 25 29 33 37 41 45



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Evolution of Entropy (3 week safety stock)

No nfo Share nfo Share

4

evels

3

evels

0

0.2

0.4

0.6

0.8

1

1 6 11 16 21 26 31 36 41 46

0

0.2

0.4

0.6

0.8

1

1 5 9 13 17 21 25 29 33 37 41 45

0

0.1

0.2

0.3

0.4

0.50.6

0.7

0.8

0.9

1

1 4 7 10131619222528313437404346

0

0.1

0.2

0.3

0.4

0.50.6

0.7

0.8

0.9

1

1 5 9 13 17 21 25 29 33 37 41 45



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Cumulative Entropy (3 week safetystock)

I I

L

l

3

L

l

0

5

10

15

20

25

30

1 5 9 13 17 21 25 29 33 37 41 45

0

5

10

15

20

25

30

1 5 9 13 17 21 25 29 33 37 41 45

0

5

10

15

20

25

30

1 5 9 13 17 21 25 29 33 37 41 45

0

5

10

15

20

25

30

1 5 9 13 17 21 25 29 33 37 41 45



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BEI Evolution (no safety stock)No I o Share I o Share

4

Levels

3

Levels

0

1

2

3

4

5

6

7

8

9

1 4 7 10131619222528313437404346

0

1

2

3

4

5

6

7

8

9

1 4 7 10131619222528313437404346

0

1

2

3

4

5

6

7

8

9

1 4 7 10131619222528313437404346

0

1

2

3

4

5

6

7

8

9

1 4 7 10131619222528313437404346



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EntropyRunningAverage (no safetystock)

I f S r I f S r

4

ls

3

ls

0

0.2

0.4

0.

0.

1

1 5 9 13 17 2 1 2 5 2 9 33 37 4 1 4 5

0

0.2

0.4

0.

0.

1

1 5 9 13 17 21 25 29 33 37 41 45

0

0.2

0.4

0.

0.

1

1 5 9 13 17 21 25 29 33 37 41 45

0

0.2

0.4

0.

0.

1

1 5 9 13 17 21 25 29 33 37 41 45



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Cumulative Entropy (no safety stock)N I S r I S r

4

L

ls

3

L

ls

0

5

10

15

20

25

30

35

40

45

1 5 9 13 17 21 25 29 33 37 41 45

0

5

10

15

20

25

30

35

40

45

1 4 7 10 131619222528313437404346

0

5

10

15

20

253

0

35

40

45

1 4 7 1 0131619222528313437404346

0

5

10

15

20

253

0

35

40

45

1 4 7 1 0131619222528313437404346



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Correlations with Inventory Errors

Inven

ory

Errors

En ropy BEI

0

40

80

120

160

0 20 40 60

orrelation

= 0.884

0

40

80

120

160

0 5 10 15

orrelation

= 0.080



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Primary Insights

Entropy provided strong measure for how supply chainsachieved stated inventory policies

Allows direct comparisons of relative effectiveness of

different safety stock levels and value of informationsharing

Entropy computational requirements on par with movingaverage calculations

Entropy provided a better indicator of how the supplychain evolves in response to changing demand situationscompared to BEI

Introduction Literature Methodology Analysis ConclusionConclusion


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Questions

& Comments

gravier and kelly 20110419

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