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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.
Highlights
Introduction and Literature SurveyIn country like large geographical area, such as India, distribution of goods such as fertilizer, cement, edible oil, sugar, food grains etc, is close in stages
Stage wise location-distribution has been attempted by Geoffrion and Graves [2], Sharma [3], Sharma and Berry [4] and Verma and Sharma [5]
Facility location problems form an important class of integer programming problems, with application in the distribution and transportation industries
Summary
In country like large geographical area, such as India, distribution of goods such as fertilizer, cement, edible oil, sugar, food grains etc, is close in stages. Goods are moved to larger sized warehouses, from larger sized warehouses to smaller sized warehouses and to markets/customers. (2014) Approaches to Solve MID_CPLP Problem: Theoretical Framework and Empirical Investigation. It is required to minimize sum total of cost of location of warehouse and cost of distribution of goods. Stage wise location-distribution has been attempted by Geoffrion and Graves [2], Sharma [3], Sharma and Berry [4] and Verma and Sharma [5]. In this paper we attempt a two-stage warehouse location problem and alongside give a novel method to solve MID_CPLP that results due to vertical decomposition developed for solution. Multistage warehouse location problems are frequently occurring in real life; see (Geoffrion and Graves [2], Sharma [3] and Sharma [10]).
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