Application of Modified Benders Decomposition to Single-Stage Multi-Commodity Multi-Period Warehouse Location Problem: An Empirical Investigation

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 subproblem 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.

Single Stage Plant-Warehouse Location Problem (SSPWLP): A State of Art Formulation

“…Dubey (2020) has established the importance of feasibility constraints such as (11) and (12). Sharma and Verma () have established the importance of Hybrid formulations (weak constraints + most promising strong constraints).…”

“…Few comments are in order here. Sharma and Namdeo (2005) did not give constraints (0a), (0b), ( 11) and (12) in their formulation for 2-stage warehouse location problem; and Sharma and Berry (2007) forgot to include constraint (12) in their formulation of SSCWLP (single stage capacitated warehouse location problem) and Sharma, Jha and Priyank (2023) (a paper submitted to IEOM 2023 Houston conference) showed that e cacy of ( 12) in problem SSCWLP was highly signi cant. We put all these classes of constraints for SSPWLP to give its state-of-art formulation.…”

Solving the Multi-Commodity Single-Stage Capacitated Warehouse Location Problem Using Bat Algorithm

“…The single-stage warehouse location problem refers to only one stage of warehouses between the plant or the manufacturer and the customer, while the multi-stage warehouse location problem refers to more than one stage of warehouses between the plant and the customer. Figure 1 shows the multi-commodity single-stage warehouse location problem [1]. Figure 1: The multi-commodity single-stage warehouse location problem…”