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On Solving General Planar Maximum Coverage Location Problem with Partial Coverage

Manish Bansal (bansal***at***vt.edu)

Abstract: 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/e^{\eta}) of the optimal solution value where e is the base of natural logarithm and \eta <= 1. We also discuss about applications of the PMCLP-PC beyond location analytics.

Keywords: maximum coverage location problem; greedy approach; pseudo-greedy algorithm; partial coverage; facility location

Category 1: Combinatorial Optimization (Approximation Algorithms )

Category 2: Applications -- OR and Management Sciences (Production and Logistics )

Category 3: Nonlinear Optimization (Other )

Citation: B12, ISE, Virginia Tech, Sept 2017

Download: [PDF]

Entry Submitted: 09/04/2017
Entry Accepted: 09/04/2017
Entry Last Modified: 01/10/2018

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