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

2

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

3

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

4

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

Cus

tom

ers

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

Cus

tom

ers

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

11

Simulation Option

Alternative Method Options

Single-Echelon Model

Echelon-Inventory Model

Graves-Willems Model

Simulation

12

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)

13

Cus

tom

ers

Strategy

Model procedureEach strategy determine where to allocate inventory.The system is considered split up in sections.

Output: Base-stock Levels

Echelon Inventory Model

14

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

Cus

tom

ers

Graves-Willems Model

15

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

16

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

18

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

19

Service Level - On-Hand Inventory

20

Bounded Demand Scenarios

21

Model Comparison

22

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

23

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

24

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

25

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

26

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

27

• 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?

28

Thank you!

Photograph courtesy of Ternium Co.