Sensitivity Testing and the Plant Location Problem

Abstract

A. wide range of models and and solution procedures are now available to the analyst concerned w~t~plant or w~rehouse location problems. While these produce an optimal solution, no expl~cIt~tatemen~~s usually made about solution stability. One large group of models concerned WIth size and~Iting problems uses the transportation model of linear programming as a solution pro~edure. ThIs paper presents a m~thod of testing th~~tability of such solutions. The problem outlmed here con~e~a plant location study and explicitly examines processing cost variations. owever, the senS!tIvity test used can be applied in general to any cost elements of a transportstion problem matrix, P LANT LOCATION studies of agricultural industries are .growing in scope and number as basic models are modified and algorithms are drawn from other fields.' Basically, such studies are concerned with the location, number, and size of processing plants to meet a set of demands at least cost. Additional particular problems, such as consideration of groups of related products [16] and short-and long-run aspects [11,7], have also been incorporated.' However, none of the studies cited has explicitly tested the sensitivity of their optimum solutions either to data variations (e.g, processing cost changes) or to the assumptions involved. Yet one such paper [6] warned that "optimal sizing and locating of facilities are very sensitive to the shapes of the warehousing (processing) cost functions." The objective of this paper is to suggest a method of exploring just such solution sensitivity.The method to be outlined was drawn from the experience of the authors with an heuristic programming problem involving plant location in an agricultural setting [4], in which explicit investigation was made of the solution sensitivity to the processing cost function used. Further, the basic method used determined the stability of the solution to change in a variety of * We appreciate helpful suggestions by Gerry Dean on an earlier draft.1 Bawden {2] has classified spatial models and outlined their data requirements and solution properties.2 Agricultural studies of interest may be conveniently grouped according to the cost minimizing objective:(1) costs of raw product assembly and processing [16,17];(2) costs of processing and distribution [6]; (3) costs of raw product assembly, processing, and distribution ill, 15J. H. 1. TOFT is research fellow in statistics at the Australian National University. P. A. CASSIDY is research officer in economics and W. O. MCCARTHY is reader in agricultural economics at the University of Queensland, Australia. critical parameters. Thus, besides overcoming weaknesses of nonconsideration of solution sensitivity, additionaf benefits accrue: (1) The change in processing costs necessary to alter the actual loca tion of processing operations can be identified; (2) effects on the solution caused by localized variations in transportation costs can be estimatedj' and (3) a parametric adaptation of the method allows mapping of optimum solutions for co...

Concave Programming Applied to Rice Mill Location

“…1 Since a review of plant location studies has appeared recenfly in the AJAE [7], it will not be duplicated here.…”