Meta-heuristics Application for Simulation Optimization of the Multi Echelon Inventory System

1. Turkish Naval Academy Meta-heuristics Application for Simulation Optimization of the Multi Echelon Inventory System Mehmet ÇAVDAR1, A.Özgür TOY2, Emre BERK3 1 Turkish Naval Academy, Institute of Naval Sciences and Engineering , İstanbul, Türkiye 2 Turkish Naval Academy, Industrial Engineering Department, İstanbul,Türkiye 3 Bilkent University, Faculty of Business Administration, Ankara, Türkiye

2. Outline • Introduction • Literature Review • Problem Definition • Simulation Model and Meta-heuristics • Numerical Results • Conclusion

3. Introduction Multi Echelon Inventory Systems Item Distributer Manufacturer Retailer Demand

4. Introduction (S-1, S) Continous Inventory Policy • High Value Items • Low Demand Rate Whenever a satisfied demand occurs, an order is placed at the same time

5. H B C I D J E K F L On hand On hand On hand On hand On order On order On order On order Introduction (S-1, S) Continous Inventory Policy Inventory Position of the Warehouse Inventory Position of the Retailer G M Demand Time = t G A

6. Introduction Stockout Condition Leadtime Dependent Backorder Backorder Decision Backorder Lostsale

7. Simulation Optimization with Search Methods & Meta-heuristics Introduction (S-1, S) Policy with Leadtime Dependent Backorder • Multi Echelon • Multi Retailer • Arbitrary Demand Arrival No Exact Solution • Constant Shelflife • Nonlinear Holding Cost & Backorder Cost

8. Literature Review (S-1, S) Single Echelon Inventory Systems (S-1, S) Multi Echelon Inventory Systems

9. Literature Review Simulation Optimization of Inventory Systems

10. DEMAND Ample Supplier Warehouse Retailers Problem Definition - Two echelon - Single item

11. Problem Definition Assumptions • (S-1,S)continous review • Full backorder at warehouse • Partial backorder at retailer(s) • Constant and deterministic leadtime • No lateral transhipment between retailer(s) • Arbitrary demand distributions • Constant shelflife at retailer level • Each demand is only for one unit

12. Problem Definition Objective Function (Minimize) • Total Cost • Warehouse • Holding Cost • Retailers • Holding Cost • Backorder Cost • Lostsale Cost

13. Problem Definition Decision Variables Optimal inventory levels to minimize the total cost • : Order up to level at warehouse • : Order up to level at retailer r (r:1..R)

14. Problem Definition Objective Function : Unit holding cost at warehouse : Unit holding cost at retailer r : Unit backorder cost/time at retailer r : Unit Lostsale cost at retailer r : Expected Onhand inventory at warehouse : Expected Onhand inventory at retailer r : Expected Backorder at retailer r : Expected Lostsale at retailer r

15. Problem Definition Nonlinear Linear Holding Cost Backorder Cost

16. Simulation Model We used “Discrete Event Simulation” • Retailer Demand Arrival • Retailer Item Arrival • Retailer Item Perish • Warehouse Item Arrival

17. Simulation Model Demands & Waiting Tolerance • Constant • Exponential Distribution • Erlang Distribution • Normal Distribution • Uniform Distribution • Weibull Distribution

18. Simulation Optimization Meta-heuristics • Simulated Annealing Algorithm • Tabu Search Algorithm • Scatter Search Algorithm

19. Simulation Optimization Simulated Annealing Algorithm • Kirk Patrick et al (1983) • To supply consistency of the metal by annealing • Fast Search (Look only one of neighbor solutions)

20. Simulation Optimization Simulated Annealing Algorithm Solution Space

21. Simulation Optimization Simulated Annealing Algorithm • Solution • A solution is neighbor of the current solution when ; • Temperature

22. Simulation Optimization Simulated Annealing Algorithm Figure for 1 Warehouse - 1 Retailer

23. Simulation Optimization Simulated Annealing Algorithm Figure for 1 Warehouse - 3 Retailers

24. Simulation Optimization

25. Simulation Optimization Tabu Search Algorithm • Glover (1986) • Fast Search (Look only neighbor solutions) • Tabu list (Avoid from the local optimum)

26. Simulation Optimization Tabu Search Algorithm Solution Space

27. Simulation Optimization Tabu Search Algorithm • Solution • A solution is neighbor of the current solution when ; • TabuList:A solution is in the tabu list if this solution is selected as current solution at last iteration

28. Simulation Optimization

29. Simulation Optimization Scatter Search Algorithm Glover et al (1997) • Take some best and diverse solutions from inital set. • Linear Combination of 2 solutions • Generate good solutions

30. Simulation Optimization Scatter Search Algorithm Solution Space RefSet ScatterSet Diverse Better Generate New Solutions

31. Simulation Optimization Scatter Search Algorithm Generate New Solutions * * * *

32. Simulation Optimization

33. C++ Programming Language • We find theoptimal inventory position levels “S”for one warehouse and retailer(s) for given parameters.

34. Numerical Results Experiments for Sensitivity Analysis • Poisson arrival process • No Shelflife • Linear Holding & Backorder Cost

35. Numerical Results Effectiveness of the Meta-heuristics 1 Warehouse 1 retailer

36. Numerical Results Effectiveness of the Meta-heuristics 1 Warehouse 3 retailers

37. Conclusion • The meta-heuristics are efficient to find the optimal/near optimal solution of the multi echelon inventory system. • Simulate Annealing is the fastest algorithm. • Tabu search is generally find the best solution among the meta-heuristics. The computational time of this algorithm is long because it computes the all neighbors‘ total costs.

38. Future Study • The future study may include lateral transshipment among retailers to analyze the effectiveness. • The model can be generalized for other inventory policies. • Another meta-heuristics can be developed to find the optimal/near optimal inventory for each SKU.

39. Turkish Naval Academy Meta-heuristics Application for Simulation Optimization of the Multi Echelon Inventory System