Vertical Decomposition Approach to Solve Single Stage Capacitated Warehouse Location Problem (SSCWLP)
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Abstract
Single Stage Capacitated Warehouse Location Problem (SSCWLP) has been attempted by few researchers in the past. These are Geoffrion and Graves [1], Sharma [2], Sharma [3] and Sharma and Berry [4]. In this paper we give a “vertical decomposition” approach to solve SSCWLP that uses Lagrangian relaxation. This way SSCWLP is broken into two versions of capacitated plant location problem (the CPLP_L and CPLP_R) by relaxing the flow balance constraints. For CPLP_R, we use well known Lagrangian relaxations given in literature (Christofides and Beasley [5] and Nauss [6]); and adopt them suitably for solving CPLP_L. We show theoretically in this paper that SSCWLP can be more efficiently solved by techniques of vertical decomposition developed in this paper than the method available in literature (Sharma and Berry [4]). Encouraging computational study is reported in this paper.
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