In this paper, we give a new method for solving the MID CPLP problem that results when vertical decomposition is applied to two-stage capacitated warehouse location problem (see Sharma and Agarwal (2014)). In the MID CPLP problem, warehouses are locatable in stage 1 and stage 2 (thus incurring fixed costs), and we incur transportation costs as goods are transported from stage 1 to stage 2. Here in MID CPLP, we minimize the sum total of the cost of warehouse location (stage 1 and stage 2) and transportation. In the method due to Sharma and Agarwal (2014), the decomposition is followed where location variables at one of the stages are relaxed, and it is reduced to LHS CPLP (Left Hand Side Capacitated Plant/Warehouse Location Problem), and reasonable bounds are obtained by the procedures given by Verma and Sharma (2007).
Thus, in the method, due to Sharma and Agarwal (2014), the problem TSCWLP is reduced to LHS CPLP, MID CPLP (that is again reduced to LHS CPLP) and an RHS CPLP. This paper reduces the problem TSCWLP to LHS LP (linear program), MID CPLP and RHS LP (linear program). It is expected to offer good computational advantages. This procedure is outlined in detail in this paper.