On Solving General Planar Maximum Coverage Location Problem with Partial Coverage

In this paper, we introduce a new generalization of the classical planar maximum coverage location problem (PMCLP) in which demand zones and service zone of each facility are represented by two-dimensional spatial objects such as circles, polygons, etc. In addition, we allow partial coverage in the foregoing generalization, i.e., covering only part of a demand zone is allowed and the coverage accrued in the objective function as a result of this is proportional to the demand of the covered part only. We denote this problem by PMCLP-PC, and present a greedy algorithm and a pseudo-greedy algorithm for it. We showcase that the solution value corresponding to the greedy (or pseudo-greedy) solution is within a factor of 1−1/e (or 1−1/eη) of the optimal solution value where e is the base of natural logarithm and η ≤ 1. We also discuss about applications of the PMCLP-PC beyond location analytics.