合同セミナー『サプライチェーンリスク管理ど人道支援ロジスティクス』
Tokyo Maritime University 07/04/2013
Optimization of the configuration of a supply chain and impact of a
supplier disruptionProf. Matsukawa , MARC Seiji
Keio University, Graduate School of Science and Technology
2
Introduction
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How to configure a supply chain? What suppliers, processes, transportation modes
to choose?
Indeed each stage of a supply chain might have several options
High cost Low costShort lead time Long lead time
Prof. Matsukawa, MARC Seiji
Introduction
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Graves and Willems (2005) explore the supply chain configuration issue
Minimization of the supply chain cost with a dynamic program
Goal of this research: Compare single and dual sourcing Analyze the effects of a supplier disruption Adapt the model to take into account fixed
ordering costs
MARC SeijiProf. Matsukawa, MARC Seiji
Table
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1. Supply chain configuration model2. Single and dual sourcing3. Impact of a disruption4. Inventory policies
5. Conclusion
MARC SeijiProf. Matsukawa, MARC Seiji
Supply chain configuration model
6 MARC SeijiProf. Matsukawa, MARC Seiji
Network model and inputs
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Network model of the supply chain
Several options at each node:
5
4
3
2
1 6
7
8
9
112
3
Cost
Lead time
External demand:• Mean• Standard deviation
Prof. Matsukawa, MARC Seiji
The optimization problem
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We try to minimize the total SC cost:
Subject to some constraints: One option chosen at each node Feasibility of the service times Respect of the service time to the external customer
Safety stock cost
Pipeline stock cost COGS
Prof. Matsukawa, MARC Seiji
The dynamic program
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The variables: options and service times At each step of the program we evaluate the
following functional equation:
Output of the program: Best options at each node to minimize the total SC
cost Optimal service times at each node
MARC SeijiProf. Matsukawa, MARC Seiji
Safety stock cost Pipeline stock cost COGS
Local VS global optimum
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Local best option option that minimizes the cost at the stage
Global best option option that minimizes the total SC cost
We compare the expected total SC costs With the local optimums: 56 482 $ With the global optimums: 54 915 $
node 1 2 3 4 5 6 7 8 9Local option 3 2 2 3 1 3 5 1 5Global option
1 5 2 3 1 3 5 1 5
Prof. Matsukawa, MARC Seiji
Single and dual sourcing
11 MARC SeijiProf. Matsukawa, MARC Seiji
Differences between single and dual sourcing
Single sourcing Dual sourcing
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Better pricing
Better and longer relationship
Better communication
Better security
Better flexibility
Maintain competition between suppliers80% 20%
MARC SeijiProf. Matsukawa, MARC Seiji
Selection of the second supplier
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First selection policy: Simplest selection policy
Better implementation in the existing program
First run Second run
MARC SeijiProf. Matsukawa, MARC Seiji
Selection of the second supplier
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Second selection policy
Better selection policy
The existing program has to be adapted
First run
MARC SeijiProf. Matsukawa, MARC Seiji
Single VS dual sourcing
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We compare the expected total SC cost Single sourcing: 53 171 $ Dual sourcing: 57 404 $
node 1 2 3 4 5 6 7 8 9First option 1 5 2 3 1 3 5 1 5Second option
2 2 1 2 2 1 2 2 2
MARC SeijiProf. Matsukawa, MARC Seiji
Impact of a disruption
16 MARC SeijiProf. Matsukawa, MARC Seiji
The calculation program
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The calculation program simulates the behavior of the SC over a certain period of time (ex: 20 weeks)
Configuration program
Calculation program
Demand realization
Disruption characteristics:• Impacted supplier• Starting time and
duration• Cost• Revenue• Profit
For example:• Best option of stage 8• Starts at t=3 for 4
periods
node 1 2 3 4 5 6 7 8 9best option 1 5 2 3 1 3 5 1 5second best option 2 2 1 2 2 1 2 2 2
0 1 2 3 4 5 6 7 8 9 1011121314151617181920708090
100110120130
real demand
MARC SeijiProf. Matsukawa, MARC Seiji
Cost calculation
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The safety stock cost:
The pipeline stock cost:
The cost of goods sold:
MARC SeijiProf. Matsukawa, MARC Seiji
Cost calculation
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Penalty cost: Recovery cost
Cost of increasing the production
capacity
Cost of holding some inventory + cost of inactivity
Cost of holding some inventory + cost of inactivity
Medium penalty rate
High penalty rate
single sourcing
dual sourcing
penalty rate
disrupted node 200 200other nodes 50 20 MARC SeijiProf. Matsukawa, MARC Seiji
Profit calculation
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The profit at time t is:
630 $
MARC SeijiProf. Matsukawa, MARC Seiji
Single VS dual sourcing without disruption
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Cost
0 1 2 3 4 5 6 7 8 9 101112131415161718192045000470004900051000530005500057000590006100063000
single sourcingdual sourcing
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20708090
100110120130
real demand
real demand
Total SC cost over the 20 weeks: Single sourcing: 1 113 410$ Dual sourcing: 1 202 583$ Difference: 8%
MARC SeijiProf. Matsukawa, MARC Seiji
Single VS dual sourcing without disruption
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Profit
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-5000
0
5000
10000
15000
20000
single sourcingdual sourcing
Total SC profit: Single sourcing: 207 699$ Dual sourcing: 118 526$ Difference: -43%
MARC SeijiProf. Matsukawa, MARC Seiji
Single VS dual sourcing with disruption
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Total SC profit: Single sourcing: -99 109$ (207 699 $) Dual sourcing: 104 214$ (118 526 $)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-50000
-40000
-30000
-20000
-10000
0
10000
20000
30000
single sourcingdual sourcing
(No disruption)
MARC SeijiProf. Matsukawa, MARC Seiji
disruption
time
Single sourcing analysis
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Cost
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2030000
35000
40000
45000
50000
55000
60000
without disruptionwith disruption
Disruption time Lead time of the disrupted node
Service time of the disrupted node
Penalty cost
MARC SeijiProf. Matsukawa, MARC Seiji
Single sourcing analysis
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Profit Without disruption: 207 699$ With disruption: -99 109$
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-50000
-40000
-30000
-20000
-10000
0
10000
20000
30000
without disruptionwith disruption
Disruption time Lead time of the disrupted node
Service time of the disrupted node
Profit overshoot
MARC SeijiProf. Matsukawa, MARC Seiji
Dual sourcing analysis
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Cost
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2020000250003000035000400004500050000550006000065000
without disruptionwith disruption
Only 20% of supply
Back to 100%
Impact of the stocks of 2nd option
Disruption time
Lead time of the disrupted node
MARC SeijiProf. Matsukawa, MARC Seiji
Dual sourcing analysis
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Total SC profit: Without disruption: 118 526$ With disruption: 104 214$ Difference: 12%
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-15000
-10000
-5000
0
5000
10000
15000
20000
25000
without disruptionwith disruption
Only 20% of supply
Back to 100%
MARC SeijiProf. Matsukawa, MARC Seiji
Inventory policy
28 MARC SeijiProf. Matsukawa, MARC Seiji
The inventory policy
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In the existing model, (s,S) policy with no fixed ordering cost S = s Orders at each period of time
We change the inventory policy K ≠ 0 We choose an (s,Q) policy
We work with the single sourcing policy on the expected costs
MARC SeijiProf. Matsukawa, MARC Seiji
The (s,Q) policy
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The inventory level:
s
t
I
MARC SeijiProf. Matsukawa, MARC Seiji
Reorder quantity Q = EOQ
Results with fixed ordering costOrders at each period (s,Q) policy
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Expected total cost: (53 171 $) 120 171 $ Inventory cost:
3901 $ 3% Pipeline + COGS:
49 270 $ 41%
Fixed ordering cost:67 000 $
56%
Expected total cost:105 504 $
Inventory cost:33 292 $
31% Pipeline + COGS:
49 270 $ 47%
Fixed ordering cost:22 942 $
22%
MARC SeijiProf. Matsukawa, MARC Seiji
Conclusion
32 MARC SeijiProf. Matsukawa, MARC Seiji
Conclusion
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Single VS dual sourcing: Single sourcing more efficient if no disruption In case of disruption, dual sourcing is way better
With fixed ordering cost: (s,Q) ordering policy has better results than every
period ordering policy The balance of the different types of cost is
different
MARC SeijiProf. Matsukawa, MARC Seiji
Conclusion
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This research produced: A configuration tool that works with different
sourcing and inventory policies A quantitative analysis of different types of SC
configuration A comparison between the different types of SC
configuration
MARC SeijiProf. Matsukawa, MARC Seiji
Further research developments
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Improve the risk management approach: Take into account a disruption risk
Improve the model to optimize more general SC
MARC SeijiProf. Matsukawa, MARC Seiji
References
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Optimizing the supply chain configuration for new productsS.C.Graves, S.P.Willems, Management Science, 2005
Optimal supply chain configuration strategies for new productsS.P.Willems, PhD thesis, MIT, 1999
Managing risks of supply chains disruptions: dual sourcing as a real optionS.Pochard, master thesis, MIT, 2000
Trial by fire: a blaze in Albuquerque sets off major crisis for cellphone giantsA.Latour, Wall Street Journal, 29 Jan 2001
To the rescue: Toyota’s fast rebound after fire at supplier shows why it is toughV.Reitman, Wall Street Journal, 08 May 1997
The power of flexibility for mitigating supply chain risksC.Tang, B.Tomlin, International Journal of Production Economics, 2008
Single or dual sourcing: decision-making in the presence of supply chain disruption risksH.Yu, A.Z.Zeng, L.Zhao, Omega, 2009
Competition in multiechelon assembly supply chainsS.M.Carr, U.S.Karmarkar, Management Science, 2005
MARC SeijiProf. Matsukawa, MARC Seiji
Thank you for your attention
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Question or remark ?
MARC SeijiProf. Matsukawa, MARC Seiji
Inventory policy
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Cycle times
1 2 3 4 5 6 7 8 90.0
1.0
2.0
3.0
4.0
5.0
6.0
0
100
200
300
400
500
600
cycle timeratio K/C
MARC SeijiProf. Matsukawa, MARC Seiji
Single VS dual sourcing without disruption
MARC Seiji39
Cost
0 1 2 3 4 5 6 7 8 9 101112131415161718192045000470004900051000530005500057000590006100063000
single sourcingdual sourcing
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20708090
100110120130
real demand
real demand
Prof. Matsukawa, MARC Seiji