A maximal covering location model in the presence of partial coverage

A maximal covering location model in the presence of partial coverage

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Article ID: iaor2005455
Country: United Kingdom
Volume: 31
Issue: 9
Start Page Number: 1515
End Page Number: 1526
Publication Date: Aug 2004
Journal: Computers and Operations Research
Authors: ,
Keywords: optimization
Abstract:

The maximal covering location problem (MCLP) addresses the issue of locating a predefined number of facilities in order to maximize the number of demand points that can be covered. In a classical sense, a demand point is assumed to be covered completely if located within the critical distance of the facility and not covered at all outside of the critical distance. Since the optimal solution to an MCLP is likely sensitive to the choice of the critical distance, determining a critical distance value when the coverage does not change in a crisp way from “fully covered” to “not covered” at a specific distance may lead to erroneous results. We allow the coverage to change from “covered” to “not-covered” within a distance range instead of a single critical distance and call this intermediate coverage level partial coverage. In this paper, we formulate the MCLP in the presence of partial coverage, develop a solution procedure based on Lagrangean relaxation and show the effect of the approach on the optimal solution by comparing it with the classical approach.

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