Upgrading edges in the maximal covering location problem

TL;DR

This paper introduces an upgraded version of the maximal covering location problem that incorporates edge length modifications on networks, aiming to optimize facility placement and edge reductions within a budget, and proposes multiple formulations and improvements for solving it.

Contribution

It formulates the NP-hard upgraded problem with new mixed-integer models, valid inequalities, and a preprocessing phase, and compares their performance on various datasets.

Findings

Proposed three mixed-integer formulations for the problem.

Developed a preprocessing phase to improve solution efficiency.

Compared formulations and enhancements through computational experiments.

Abstract

We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the length of the edges can be reduced at a cost, subject to a given budget. Hence, we have to decide on: the optimal location of p facilities and the optimal edge length reductions. This problem is NP-hard on general graphs. To solve it, we propose three different mixed-integer formulations and a preprocessing phase for fixing variables and removing some of the constraints. Moreover, we strengthen the proposed formulations including valid inequalities. Finally, we compare the three formulations and their corresponding improvements by testing their performance over different datasets.