Multi-Echelon Multi-product Inventory Policy in a …€¢ Simchi-Levi, D., Kaminsky, P. and...
Transcript of Multi-Echelon Multi-product Inventory Policy in a …€¢ Simchi-Levi, D., Kaminsky, P. and...
Juan Iocco
Advisor: Amanda J. Schmitt, PhD
Multi-Echelon Multi-product Inventory Strategy in a Steel Company
May 21, 2009 MIT, ESD
Master of Engineering in Logistics
Agenda
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IntroductionTernium’s ProblemTernium’s Three-Echelon SystemTheory Background: Four Models EvaluatedMethod applied
Simulation Alternative Methods
ResultsInventory Allocation Best SolutionsSensitivity Analysis and Method Comparisons
Conclusions
Ternium’s Problem
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Ternium : multi-product three-echelon production system.
Safety Stock only first in the stage.
Customers need reduced service time and increased service level
Thus: Increased Safety Stock is needed
However: Ternium needs reduced Safety Stocks Costs.
There is no analytical solution for determining multi-echelon distribution systems.
Objective
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Determine where to allocate safety stocks.
Compare alternative methods’ results.
Ternium’s Three Downstream Echelons
Slabs /Hot Rolled Steel
Cold Rolled Steel
Coated Steel
Customized Coated Steel
Thesis’ Objective
Iron ore / Coal
Photographs courtesy of Ternium Co.
Ternium’s Three Downstream Echelons
Slabs /Hot Rolled Steel
Cold Rolled Steel
Coated Steel
Customized Coated Steel
Thesis’ Objective
Iron ore / Coal
Photographs courtesy of Ternium Co.
Ternium’s Three-Echelon System
(≈10,000 SKU) (≈15,000 SKU) (≈25,000 SKU)
Cold Rolled Steel
Coated Steel Customized Coated Steel
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Product 1Product 2
Product 3
Product 4
Product 5
Product 6
Product 7
Product 8
Product ..
Product ..
Product ..
Product ..
Product “n”
Echelon: 1 2 3
3-Echelon System Selected Case
Cold Rolled Steel
Coated Steel Customized Coated Steel
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Echelon: 1 2 3
Multi-Echelon System Parameters
• Lead Time: 3 weeks, 2 weeks and 1 week (constant)
• Service Time < 1 week
• Service Level >= 95%
• Demand: normally distributed, independent, Coefficient of Variance = 0.5
• 3 Holding Cost Scenarios (“L,L,L”, “L,L,H” and “L,H,H”)
• 3 Bounded Demand Scenarios: 50%, 100% and ∞
Theory: options evaluated
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Simulation Option
Alternative Method Options
Single-Echelon Model
Echelon-Inventory Model
Graves-Willems Model
Simulation
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Model characteristics (general for all the models)
1-3-5 facilities distribution three-echelon systemBase-stock model
Model procedureRun each scenario1,000 periods (weeks)Program to solve automatically ≈ 1,000 -1,400 inventory allocation scenarios
Output: average period Service Level, Holding Cost and
On-Hand Safety Stock
Single Echelon-Model (Split System)
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Strategy
Model procedureEach strategy determine where to allocate inventory.The system is considered split up in sections.
Output: Base-stock Levels
Echelon Inventory Model
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Model procedureAssumes a single decision maker and access to safety-stock information.Calculate the echelon position safety stock (ESS).
Output: Base-Stock Level at every echelon
Source: Schimchi-Levi D., Chen X. & Bramel J. (2005)
ESS1ESS2ESS3
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Graves-Willems Model
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Model procedureSolve spanning tree inventory systems.Inputs: Holding Costs, Lead Time, customer Service Time, demand parameters.
Output: facilities’ Service Time (Base-stock levels)
Source: Graves S. C., & Willems S. P. (2000)
Solution
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Determine Where to Allocate SS
Construct a simulation model.
Scenarios, Best solution and Sensitivity Analysis.
Compare alternative methods’ results
Calculate base-stock levels with alternative methods.
Simulate and compare results.
Results: Allocation Strategies
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iji
ijsim LT
SSk
σ×= - SS = Safety Stock at Echelon i, facility j
- LTi = Lead Time of Echelon i- σij= Demand standard deviation at echelon i, facility j.
Service Level-Holding Cost Efficient Frontier
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Service Level - On-Hand Inventory
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Bounded Demand Scenarios
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Model Comparison
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Difference in holding cost against best solutions found with
simulation.
Alternative Methods % Variation
Holding Cost
Echelon Inventory Model 8.2%
Graves-Willems Model 9.7%
Single-Echelon 1 35.0%
Single-Echelon 2 15.4%
Single-Echelon 3 18.5%
Conclusions: Allocation Strategy
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Simulation worked well, but results are sensitive to cost parameter.Best results presented.General behavior related to cost.Similar behavior changing with risk-pooling factors (more correlation or serial 3-Echelon systems).
Deep understanding of the demand is critical.Strong assumptions made about cost and correlation.Characterization of demand is a “must”.
Keep safety stock just in the first stage is a bad decision.Strategy showed to be 35% more expensive.
Conclusions: Allocation Strategy
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Bounded demand strategies are good alternatives.We showed that cost reductions ranging 20% are possible. Important to explore other contract clause alternatives (buy-back, cost shearing, etc).
On-hand inventory as only metric is not good to manage inventories. Inventory turnover and total inventories are classic metrics.It tend to make people thinks that On-Hand inventory and Service Level are proportionally related .
Conclusions: Method Comparison
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Simulation allowed to find the best results.Build the Efficient Frontier (and find the best results).
Compare the different methods.
But, find the best results was not easy, could be complicated to apply in bigger ME systems.
Echelon-inventory and Graves –Willems method produced the lowest alternative holding-cost results.
In average, were the closest method to the best solution.
In the case of the echelon-inventory model, it was needed to tuned the parameters with the simulation to get SL close to 95%.
Conclusions: Method Comparison
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Single-Echelon methods do not perform well as a standalone method.We showed that average extra cost was far from other simulation (16 to 35%).
Decide which single-echelon strategy apply is difficult.
References
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• Bertsimas, D., and Freund, R. (2004). Data, Models, and Decisions: the Fundamentals of Management Science. Belmont, MA: Dynamic Ideas.• Chacon, G., and Terwiesch, C. (2006). Matching Supply with Demand: An Introduction to Operations Management (2nd ed.). New York, NY: McGraw Hill Companies.• Chopra, S., and Meindl, P. (2007). Supply Chain Management (3rd ed.). Upper Saddle River, NJ: Pearson Education, Inc.• Clark, A. J., and Scarf, H. (1960). Policies for a Multi-Echelon Problem. Management Science, 6 (4), 475-490.• Graves, S. C., and Willems, S. P. (2000). Optimizing Strategic Safety Stock Placement in Supply Chains. Manufacturing & Services Operations Management, 2 (1), 68-83.• Graves S. C., and Willems, S. P. (2003). Erratum: Optimizing Strategic Safety Stock Placement in Supply Chains. Manufacturing & Service Operations Management, 5 (2), 176-177.• Hillier, F., and Lieberman, G. (2005). Introduction to Operations Research (8th ed.). New York, NY: McGraw Hill Companies.• Pagh, J.D., and Cooper, M. (1998). Supply Chain postponement and speculation strategies: How to choose the right strategy. Journal of Business Logistics, 19 (2).• Silver, E., Pyke, D. and Peterson, R. (1998). Inventory Management and Production Planning and Scheduling(3rd ed.). Hoboken, NJ: John Wiley & Sons, Inc.• Simchi-Levi, D., Chen X. and Bramel, J. (2005). The Logic of Logistics (2nd ed.). New York, NY: Springer.• Simchi-Levi, D., Kaminsky, P. and Simchi-Levi, E. (2008). Designing and Managing the Supply Chain: Concepts, Strategies, and case studies (3rd ed.). New York, NY: McGraw Hill Companies.• Snyder, L. V. (2006). User’s Guide for BaseStockSim. Software Version 2.4. [WWW document]. URL http://www.lehigh.edu/~lvs2/download/basestocksim.html (visited 2009, May 2).• PowerChain Inventory Academic version 3.0 Manual. [WWW document]. URL http://web.mit.edu/lfmrg3/www/archives/sipmodel/index.htm (visited 2009, May 2).• Taylor, D. A., (2004). Supply Chains: A Manager’s Guide. Boston, MA: Addison-Wesley. • van Houtum, G. J. (2006). Multi-Echelon Production/Inventory Systems: Optimal Policies, Heuristics, and Algorithms, INFORMS Tutorials in Operations Research.• Winston, W. L. (2004). Operations Research: Applications and Algorithms (4th ed.). Belmont, CA: Thomson Brooks/Cole.
Any questions?
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Thank you!
Photograph courtesy of Ternium Co.