Robust solutions for supply chain management: simulation, optimization & risk analysis Jack Kleijnen & Bert Bettonvil Tilburg University, The Netherlands
Fredrik Persson Linköping Institute of Technology, Sweden April 2003 Acknowledgment: KLICT
Overview Robustness: Taguchi (Toyota cars) Case study: SCM simulation for Ericsson Sweden 1. Screening: Shortlist of important factors 2. Controllable versus environmental factors 3. Controllable: Central composite design 4. Environmental: Latin Hypercube Sampling 5. ‘Optimize’ controllables (see 4): Minimize mean & variance, over LHS (see 5) 6. Confidence region: Bootstrap 7. Select ‘robust’ solution 3/25/2003
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Introduction Kleijnen & Gaury (2003): 1. Derive optimal solution for base scenario Estimate sensitivity to environmental changes 2. Academic example Now: 1. Derive optimal solution accounting for all possible environments 2. Ericsson case study Taguchi: Taguchi: Physical products design Our simulation: Same philosophy; other methods Reason: More factors; more combinations 3/25/2003
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Screening procedures Literature: Literature: Dean & Lewis (2003), Springer Campolongo, Kleijnen & Andres (2000), Wiley Bettonvil & Kleijnen (1997): Sequential bifurcation (SB), EJOR Now: 1. SB for random simulation 2. Case study: study: see next slide
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Case study: Ericsson’s three supply chains (a)
Test
Circuit Board Manufacturing (b)
SMD and Vision Test
Test
Circuit Board Manufacturing
(c)
Test
Wave Soldering
Test
SMD and Vision Test
Test
Test
Frame Soldering Assembly
Function Test Time Test
Frame Assembly
Function Test Time Test
Final Test
Assembly
Final Test
Assembly
Final Test = Test = Operation
Circuit Board Manufacturing
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Case study: Simulation model for Current supply chain Scrap Rework
Scrap Rework
Yield
Scrap
Scrap
Rework Yield
Flowof materials
Rework Yield
Scrap Rework
Yield
Yield
75 % Circuit board manufacturing
SMDand vision test
Test
Frame assembly Function test
Time test
Assembly
Final test
= Test station = Buffer = Operation 3/25/2003
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Case study: study: Continued Our focus: Single output (mean total cost) SteadySteady-state mean: Drop transient outputs 16 weeks: 4 weeks dropped Software: ‘Taylor ‘Taylor II’ Problem: PRN uncontrolled; no CRN
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Screening: Sequential Bifurcation Screening: Old SC: 92 factors; Current SC: 78; Next SC: 49 Standardize factors: -1, +1 Most important factor: Highest main effect SB assumptions: assumptions: 1. Main effects & possibly twotwo-factor interactions Simulate only two values per factor 2. Known signs of main effects: Define factor values such that main effects are nonnon-negative (no cancellation) 3: No main effect j: No interactions with factor j Replicate each scenario m times (Case study: m = 5) 3/25/2003
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SB results 1. Old model: Only 21 scenarios simulated Number of important factors: 11 Most important factor is #92 (demand): 8,087,149 Least important factor is #88 (yield): 241,809 ‘Unimportant effects: < 12,792 2. Current model: 9 important factors 3. Future model: 7 3/25/2003
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Robustness: Robustness: DOE SB results: 3 controllable factors; 6 environmental factors Now: Add one group of unimportant unimportant controllable factors Add one group of unimportant unimportant environmental ,, 1. SecondSecond-order polynomial metamodel in 4 controllable factors Reduced CCD: CCD: only half of the ‘star’ (sub)design 2. LHS for 10 random scenarios of 7 environmental (noise) Sub 1 & 2: Cross both designs (Taguchi) Do not replicate: Pure error is smaller than LHS variation Computer time for Current model: 42 hours (600Mhz PC) 3/25/2003
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Robustness: Analysis of DOE No estimation of interactions between controllable & environmental factors: No dynamic control (‘flexibility’) Box constraints (5 (5%, %, 25% changes): Lagrnagian Unique minimum or ridge: ridge: SecondSecond-order derivatives Estimate from crossed design; see preceding slide Repeat for output’s estimated variance (instead of mean) Are optimal controls identical for mean & variance? Confidence region: Bootstrap (inexpensive resampling of original simulation outputs) Let management decide! 3/25/2003
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Robustness: three supply chain configurations SB results: Old model:
1 extra important controllable: Expand CCD 1 extra environmental factor: Same LHS
Future model:
Same controllable factors as Current Fewer environmental factors: Same LHS
Note: Two extreme scenarios do give extreme outputs Conclusion: ‘Optimized’ Future model gives ‘best’ output (lowest mean & variance) 3/25/2003
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Robust versus optimal solution Optimal solution assuming a single (base) scenario Robust solution accounting for all possible scenarios Does risk analysis make a difference? Numerical results: See forthcoming paper
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Conclusions & further research A new methodology, developed & applied Further research: 1. SB for multiple outputs 2. Robustness including constrained multiple outputs 3. Our interpretation of Taguchi: Correct? Reference: Download from
http://center.UvT.nl http://center.UvT.nl/staff/ nl/staff/kleijnen /staff/kleijnen/papers.html kleijnen/papers.html
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