Tradeoff Analysis for An Inventory-Location Distribution Network System

1. Tradeoff Analysis for An Inventory-Location Distribution Network System Department of Management Sciences and Decision Making, Tamkang University Shu-Hsien,Liao (廖述賢) Chia-Lin Hsieh (謝佳琳) TAAI 2008

2. Outline • Research Problem • The Location-Inventory Problem • Theorem • Mathematical Formulation of the Location-Inventory Model • Methodology • NSGAII-based Algorithms for the Inventory-Location Model • Preliminary Results and Perspectives Research Problem Theorem Methodology

3. Supply Chain Distribution Network Design- Facility Location Problem Research Problem

4. Agile Supply Chain (Responsiveness or Customer Service Level) Lean Supply Chain (Efficiency or Cost) Four Strategic Planning Issues in Supply ChainDistribution Network Design Location-Inventory Problems (LI) Location-Routing Problems (LR) Inventory-Routing Problems (IR) Research Problem

5. Inventory Aggregation Buyers / Demand Zones Potential Regional DCs Single Supplier 1 Capacitated DCs 1 2 Pooled Safety Stock Inventory 1 3 j i J I Our Centralized Location-Inventory Problem based on Inventory Aggregation A single supplier, multiple-products, two-echelon SCN design problem under Inventory Aggregation Research Problem

6. Overview of our Integrated Location-inventory Model

7. Buyer-Supplier Cost Structure of Centralized Distribution Network System Research Problem

8. General Assumptions (1/2) • Locations of buyers and DCs are discrete and have been determined before starting the allocation resources. (Discrete DCs/buyers) • Buyers are provided several products but one specific product for a buyer should be shipped from a single DC. (Single Source) • Demands at buyers are uncertain. (Stochastic Demand) • Safety-stock inventory for all the buyers served by a DC is aggregated at that DC. (Inventory Aggregation) Theorem

9. General Assumptions (2/2) • Storage capacities at the supplier is unlimited but are limited at DCs where their maximum capacities are known. (Uncapacitated Supplier/Capacitated DCs) • There is no reverse flow from buyers to DCs even back to supplier. (No Reverse Flow) • The vehicle routing problem is not considered. (No Vehicle Routing Problem) • No transshipment point between DCs and buyers. (No Transshipment ) Theorem

10. Multi-Objective Location-Inventory Problem (MOLIP) • Given: • A set of DCs • A set of buyers • Demand per buyer • Distribution Cost • Operating Cost per DC • Facility Capacity per DC • Objectives: • DCs that should operated & buyers that should be attended by each DC for: • Minimizing total cost • Maximizing service level • Constraints: • The sum of the demands attended by each retailer does not exceed the DC’s capacity Theorem- BOLIP Model

11. Theorem- BOLIP Model

12. Total Cost Objective Function Facility Operating Cost Transportation Cost Ordering Cost Transportation Cost Cycle Stock Cost Safety Stock Cost Theorem- MOLIP Model

13. Non-linear Function Rewrite Z1 as Theorem- MOLIP Model

14. Multi-objective Location Inventory Problem (MOLIP) Total Objective Functions • Minimizing total cost • Maximizing Volume Fill Rate • Maximizing • Service Responsiveness

15. Constraints Single sourcing assignment Fixed-charge Capacity restriction

16. NSGA-II Features • Concept of Domination Theorem- NSGAII

17. Non-dominated sorting Concept of Domination NSGA-II Features • Fast Non-Dominated Sorting • which performs a clever sorting strategy. Theorem- NSGAII

18. NSGA-II Features Crowding Distance Assignment which estimates the density of solutions in the objective space. Cuboid for solution i, formed by joining the neighboring solutions in its non-dominated front Theorem- NSGAII

19. ensures good solutions lie in better nondominated fronts ensures diversity in a particular non-dominated front with higher crowding distances NSGA-II Features Crowded Tournament Selection Operator instead of comparing two solutions on the basis of their fitness function values, they are compared on the basis of the ranks of their non-dominated fronts, and their crowding distances Theorem- NSGAII

20. NSGA-II Algorithm Theorem- NSGAII

21. Chromosome Representation: Each solution of the MOLIP is encoded in a binary string of length m=|I| if DC i is open (value of 1) or closed (value of 0). Methodology

22. Methodology

23. Model Applications and Preliminary Results Number of DC=15, Number of Buyers= 50, Dmax=25 Preliminary Results

24. Preliminary Results

25. Performance Evaluation of the Hybrid GA for MOLIP Preliminary Results

26. Preliminary Results

27. Preliminary Results

28. Model experiments with sensitivity analysis - sensitivity analysis of varying coverage distances

29. Model experiments with sensitivity analysis - sensitivity analysis of unit inventory holding cost Preliminary Results

30. Model experiments with sensitivity analysis - sensitivity analysis of varying location capacity Preliminary Results

31. Perspectives and Expected Results • Complete data collection and performance analysis • Perform scenario and sensitivity analysis • Larger problem sets need to be evaluated • “If NSGAII-based LI algorithm offers practical advantages that still possessed efficient or effective solutions?” is under investigation • Compared with other MOGA-based methodology e.g. SPEAII- Zeitler 2000 or PAES (Knowles 2000) Preliminary Results

32. The End 敬請指教!

33. Assignment Rule • Rule 1. If the buyer i is covered (i.e., there are DCs within a coverage distance of ), it is assigned to the DC with sufficient capacity (if exists) which can serve it with the minimal difference between the remaining capacity of an open DC j and the demand flow dij of the buyer i through DC j. That is, a DC is tried to be assigned as full as possible. Rule 2. If the buyer i cannot be covered or there is no successful assignment from the coverage set i, it is then assigned to the candidate DC (with sufficient capacity) that increases the total cost by the least amount, regardless of its distance to the DC if possible. Methodology

34. Similar to Data from Shen & Daskin (2005)

35. Future Researches • Inclusion of other decisions • Inventory • replenishment policies • frequency and size of the shipments • including stockout and backorder costs • Transportation • Route • Vehicle modes • The proposed GA points to a number of directions for future work • Exploration and evaluation on a variety of problems with varying sizes • The comparisons of GA to other heuristics such as other MOEA, Lagrangian relaxation, soft computing, methods