Approaches to Solve MID_CPLP Problem: Theoretical Framework and Empirical Investigation

Abstract

In two-stage warehouse location problem, goods are moved from plants to warehouses at stage-1 (which are larger sized warehouses), and from there to warehouses at stage-2 (which are smaller sized warehouses); and finally to the markets. We aim to minimize the sum of location costs of the warehouses at stage-1 and stage-2; plus the total distribution cost of goods to the markets. In this paper two-stage capacitated warehouse location problem (TSCWLP) is vertically decomposed into the smaller problems, which is attained by relaxing the associated flow balance constraints. This leads to three different versions of Capacitated Plant Location Problem (CPLP) referred as RHS_CPLP, MID_CPLP and LHS_CPLP (Verma and Sharma REF _Ref387068711 \r \h [1]). In this paper MID_CPLP is reduced to RHS_CPLP and a single constraint 0-1 Knapsack problem by relaxing a difficult constraint. Interesting results and conjectures are given. Later two more valid constraints are added to MID_CPLP which are relaxed further to get additional results.