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Replacing continuous demand with discrete demand in a competitive location model
Author(s) -
Drezner Tammy,
Drezner Zvi
Publication year - 1997
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/(sici)1520-6750(199702)44:1<81::aid-nav5>3.0.co;2-i
Subject(s) - mathematical optimization , facility location problem , location model , computer science , computation , set (abstract data type) , simple (philosophy) , 1 center problem , demand curve , function (biology) , continuous modelling , mathematics , algorithm , operations research , economics , mathematical analysis , philosophy , epistemology , evolutionary biology , microeconomics , biology , programming language
Location models commonly represent demand as discrete points rather than as continuously spread over an area. This modeling technique introduces inaccuracies to the objective function and consequently to the optimal location solution. In this article this inaccuracy is investigated by the study of a particular competitive facility location problem. First, the location problem is formulated over a continuous demand area. The optimal location for a new facility that optimizes the objective function is obtained. This optimal location solution is then compared with the optimal location obtained for a discrete set of demand points. Second, a simple approximation approach to the continuous demand formulation is proposed. The location problem can be solved by using the discrete demand algorithm while significantly reducing the inaccuracies. This way the simplicity of the discrete approach is combined with the approximated accuracy of the continuous‐demand location solution. Extensive analysis and computations of the test problem are reported. It is recommended that this approximation approach be considered for implementation in other location models. © 1997 John Wiley & Sons, Inc.