A mathematical model for the coverage location problem with overlap control.

The Coverage Location Problem (CLP) seeks the best locations for service to minimize the total number of facilities required to meet all demands. This paper studies a new variation of this problem, called the Coverage Location Problem with Overlap Control (CLPOC). This problem models real contexts related to overloaded attendance systems, which require coverage zones with overlaps. Thus, each demand must be covered by a certain number of additional facilities to ensure that demands will be met even when the designated facility is unable to due to some facility issue. This feature is important in public and emergency services. We observe that this number of additional facilities is excessive in some demand points because overlaps among coverage zones occur naturally in CLP. The goal of the CLPOC is to control overlaps to prioritize regions with a high density population or to minimize the number of coverage zones for each demand point. In this paper, we propose a new mathematical model for the CLPOC that controls the overlap between coverage zones. We used a commercial solver to find the optimal solutions for available instances in the literature. The computational tests show that the proposed mathematical model found appropriate solutions in terms of number of demand points with minimum coverage zones and sufficient coverage zones for high demand points.