Planar Maximum Coverage Location Problem with Partial Coverage, Continuous Spatial Demand, and Adjustable Quality of Service

TL;DR

This paper introduces a generalized planar maximum coverage location problem allowing partial coverage, adjustable service quality, and complex demand and service zones, with new algorithms and theoretical insights for continuous spatial optimization.

Contribution

It develops greedy and pseudo-greedy algorithms with approximation ratios, and proposes exact algorithms for specific cases, extending prior work on fixed QoS scenarios.

Findings

Approximation algorithms with proven ratios for PMCLP-PC-QoS.

Exact algorithms for rectangle-based demand and service zones.

Computational results demonstrating algorithm performance.

Abstract

We consider a generalization of the classical planar maximum coverage location problem (PMCLP) in which partial coverage is allowed, facilities have adjustable quality of service (QoS) or service range, and demand zones and service zone of each facility are represented by two-dimensional spatial objects such as rectangles, circles, polygons, etc. We denote this generalization by PMCLP-PC-QoS. A key challenge in this problem is to simultaneously decide position of the facilities on a continuous two-dimensional plane and their QoS. We present a greedy algorithm and a pseudo-greedy algorithm for it, and provide their approximation ratios. We also investigate theoretical properties and propose exact algorithms for solving: (1) PMCLP-PC-QoS where demand and service zones are represented by axis-parallel rectangles (denoted by PMCLP-PCR-QoS), which also has applications in camera surveillance and satellite imaging; and (2) one dimensional PMCLP-PC-QoS which has applications in river cleanups. These results extend and strengthen the only known exact algorithm for PMCLP-PCR-QoS with fixed and same QoS by Bansal and Kianfar [INFORMS Journal on Computing 29(1), 152-169, 2017]. We present results of our computational experiments conducted to evaluate the performance of our proposed exact and approximation algorithms.