Abstract
In the past, researchers have applied Bender’s decomposition to distribution problem and used feasibility constraint to speed up the performance of Bender’s decomposition. Further, the application of Branch and Bound to single-stage multi-commodity single-period warehouse location problem (SSMCSPWLP) with strong constraints has shown that they are more effective. It was also shown in the previous research (in the context of Branch and Bound Methodology) that hybrid formulation for the single-stage single-period multi-commodity warehouse location problem yielded superior results. In this paper we apply Benders’ decomposition to strong and weak formulations of single-stage multi-commodity multi-period warehouse location problem (SSMCMPWLP). As suggested in the previous literature we put feasibility constraints in the pure integer sub- problem to speed up the performance of Benders’ decomposition. We also develop an additional cut (constraint that is again added to pure integer sub-problem) and show that it further speeded up Benders’ Decomposition. This research led to the possibility of applying Benders’ Decomposition to the hybrid formulation of SSMCMPWLP in future.
Highlights
Introduction and Literature SurveyWarehouse location-allocation problem is a well-known real life problem encountered in the areas like supply chain of FMCG, Food Corporation of India (FCI), fertilizer, and cement distribution system etc
For the sake of completeness we describe the Benders’ decomposition here in brief. (Details can be seen in Sharma [3].) The problem SSCMCMPWLP is similar to the following general mix of 0 - 1 Integer Linear Program (ILP)
Twin means both feasibility and additional cut constraint are put in pure integer linear program (ILP) and without means only the feasibility constraint is put in the pure ILP sub problem
Summary
Warehouse location-allocation problem is a well-known real life problem encountered in the areas like supply chain of FMCG, FCI, fertilizer, and cement distribution system etc. The literature on CPLP as given by Francis & Goldstein [7], Salkin [8] is abundant This type of problem is handled and solved by researchers by both the exact solution methods and heuristic approaches. Sharma & Agrawal [15] used vertical decomposition to solve the two staged capacitated warehouse location problem (TSCWLP) which was attempted by Keskin and Uster [6] using heuristic based scatter search algorithm. Geoffrion & Graves [2] concluded in their paper the remarkable effectiveness of Bender’s Decomposition as a computational study for multi commodity warehouse location problems, the numeric results showed that only a few cuts are needed to find and verify a solution within one or two tenths of one percent of the global optimum. Sharma et al [18] have proved that the Benders’ decomposition is more effective on strong formulation of SSCWLP as compared to weak formulation in terms of number of iteration and Benders’ decomposition is more effective on weak formulation of SSCWLP in terms of execution time
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