Academic journal article Global Business and Management Research: An International Journal

Vertical Decomposition Approach for Two Stage Capacitated Warehouse Location Problems

Academic journal article Global Business and Management Research: An International Journal

Vertical Decomposition Approach for Two Stage Capacitated Warehouse Location Problems

Article excerpt

Introduction

In any organization, one of the most important strategic decisions is to locate facilities viz. factories, plants or warehouses. While locating a facility, the most prioritized criterion is a good service level. However, achievement of an economic optimality is also a key decisive factor. Based on the number of stages between the producing facility and the market, there are different types of facility location problems like simple plant location problem, single stage / two stage warehouse location problem and multistage facility location problem. A latest review of literature on location problems can be found in Sahin and Sural (2007) and ReVelle et al. (2008). Multistage warehouse location problems are frequently occurring in real life (see: Geoffrion and Graves, 1974; Sharma, 1991; and Sharma, 1996). In this work, we will discuss Two Stage Capacitated Warehouse Location Problem (TSCWLP). If the distance between the plants and markets is too high and there are two sets of warehouses between them, their intermediate distances (plants--warehouse 1 (whs-1) warehouse 2 (whs-2)--markets) become comparatively less. Here it is assumed that warehouses have finite capacity and single commodity is considered for distribution.

The locations of the potential warehouses are known and each has a fixed cost associated with it. The problem is to choose such warehouses for which (fixed location cost associated with (whs-1 and whs-2) + transportation cost from (plants to whs-1 + whs-1 to whs-2 + whs-2 to markets)) is minimum while satisfying the demands at each point.

Formulations of TSCWLP Problem formulation

TSCWLP studied by Sharma and Namdeo (2005) uses the new formulation style (Sharma and Sharma, 2000) to develop a variety of constraints that link real and 0-1 integer variables. They have also developed some strong constraints based on Sharma and Berry (2007).

Constants Definition

Here index 'h' is used for plants, 'i' for whs-1, 'j' for whs-2 and 'k' for markets.

[D.sub.k]:          Demand for the commodity at market 'k'
[d.sub.k]:          [D.sub.k] / [SIGMA] [D.sub.k], Demand at market
                      'k' as a fraction of total market demand.
fws[1.sub.i]:       Fixed cost of locating a stage 1 warehouse at 'i'
fws[2.sub.j]:       Fixed cost of locating a stage 2 warehouse at 'j'
[S.sub.h]:          Supply available at plant 'h'
[s.sub.h]:          [S.sub.h] /[SIGMA][D.sub.k], Supply available at
                      plant 'h' as a fraction of the total market
                      demand.
CAPWS[1.sub.i]:     Capacity of a stage 1 warehouse 'i'
CAPWS[2.sub.j]:     Capacity of a stage 2 warehouse 'j'
capws[1.sub.i]:     G4PWS[1.sub.i] / [SIGMA] [D.sub.k], Capacity of
                      whs-1 at ' i' as a fraction of total market
                      demand.
capws[2.sub.j]:     CAPWS[2.sub.j] / [SIGMA] [D.sub.k], Capacity of
                      whs-2 at 'j' as a fraction of total market
                      demand.
cpws[1.sub.hi]:     Cost of transporting [SIGMA][D.sub.k] goods from
                      plant 'h' to whs-1 'i'
cws1ws[2.sub.ij]:   Cost of transporting [SIGMA][D.sub.k] goods from
                      whs-1 'i' to whs-2 'j'
cws2[m.sub.jk]:     Cost of transporting [SIGMA][D.sub.k] goods from
                      whs-2 'j' to market 'k'

Variable Definition

XPWS[1.sub.hi]:     Quantity of commodity transported from plant 'h'
                      to whs-1 'i'.
xpws[1.sub.hi]:     XPWS[1.sub.hi] /[SIGMA][D.sub.k], Quantity
                      transported from 'h' to ' i' as fraction of
                      total demand.
XWS1WS[2.sub.ij]:   Quantity of commodity transported from whs-1 'i'
                      to whs-2 'j'.
xws1ws[2.sub.ij]:   XWS1WS[2.sub.j] /[SIGMA][D.sub.k], Quantity
                      transported from 'i' to 'j' as fraction of total
                      demand
XWS2Mjk:            Quantity of commodity transported from whs-2 'j' to
                      market 'k'
xws2[m. … 
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