The Gradual Minimal Covering Location Problem

Abstract

The minimum covering location problem with distance constraints (MCLPDC) deals with locating a set of undesirable facilities on a geographical map, where there is a given minimum distance between any pair of located facilities. The objective is to minimize the total population covered by the located facilities. The gradual coverage extends the classic definition of the coverage and is able to better model many real-world applications. Traditionally, a covering radius is defined within which the population node is fully covered and beyond that it is not covered at all. This setting may not be applicable in practice because the coverage usually decreases gradually with an increase in the distance. We propose a mixed-integer program for the problem and a threshold accepting heuristic as the solution method, particularly, for large problem instances that the model is of no use for generating even feasible solutions. We conduct computational experiments on instances with up to 10,000 nodes. The outcomes indicate that the heuristic delivers quality solutions and outperforms the solver Gurobi.

Keywords: minimal coverage, gradual covering, undesirable facility, facility location, distance constraint