Minmax regret maximal covering location problems with edge demands

TL;DR

This paper introduces a minmax regret model for a maximal covering location problem on networks with uncertain, edge-distributed demand, providing polynomial algorithms and computational insights.

Contribution

It proposes a novel minmax regret model for edge-demand distributed location problems and offers polynomial algorithms for specific demand scenarios.

Findings

Algorithms effectively minimize maximal regret under demand uncertainty.

Computational study demonstrates the approach's potential and limitations.

Illustrative examples validate the methodology.

Abstract

This paper addresses a version of the single-facility Maximal Covering Location Problem on a network where the demand is: (i) distributed along the edges and (ii) uncertain with only a known interval estimation. To deal with this problem, we propose a minmax regret model where the service facility can be located anywhere along the network. This problem is called Minmax Regret Maximal Covering Location Problem with demand distributed along the edges (MMR-EMCLP). Furthermore, we present two polynomial algorithms for finding the location that minimises the maximal regret assuming that the demand realisation is an unknown constant or linear function on each edge. We also include two illustrative examples as well as a computational study for the unknown constant demand case to illustrate the potential and limits of the proposed methodology.