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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
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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?
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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
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Manufacturer
Wholesaler
Retailer
End
Consumer
Distributor
Transportation
Delays
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Step up Demand Scenario
Introduction Literature MethodologyMethodology Analysis Conclusion
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
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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
No informationsharing
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
No informationsharing
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
No informationsharing
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
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& Comments
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