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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.
Highlights
Introduction and Literature ReviewThe problem considered in this work is referred to as the single stage capacitated warehouse location problem (SSCWLP), which arises when the distances between plants and markets are large and it becomes necessary to route the supplies through warehouses
One involving flow from plants to warehouse (CPLP_L), two involving flow from warehouse to markets (CPLP_R). Using this approach we use the theory developed for capacitated plant location problem (CPLP) (Cornuejols, Sridharan, & Thizy [16]) (by suitably extending it to adopt to new version of CPLP) to solve the original SSCWLP by using a Lagrangian relaxation
We name this approach as vertical decomposition approach, because the full SSCWLP is decomposed into two parts
Summary
The problem considered in this work is referred to as the single stage capacitated warehouse location problem (SSCWLP), which arises when the distances between plants and markets are large and it becomes necessary to route the supplies through warehouses (of limited capacities). A realistic variant to the problem that measure customer satisfaction is attempted by Eskigun et al [11] where an outbound supply chain network is designed considering operational dynamics of lead times, etc They provide a Lagrangian based heuristic, which gives good quality solutions. One involving flow from plants to warehouse (CPLP_L), two involving flow from warehouse to markets (CPLP_R) Using this approach we use the theory developed for capacitated plant location problem (CPLP) (Cornuejols, Sridharan, & Thizy [16]) (by suitably extending it to adopt to new version of CPLP (referred to as CPLP_L)) to solve the original SSCWLP by using a Lagrangian relaxation.
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