Integer programming models for the semi-obnoxious p-median problem

TL;DR

This paper introduces twelve integer linear programming models for a semi-obnoxious p-median problem with minimum distance constraints, comparing their performance using Gurobi on a large dataset.

Contribution

It develops and compares multiple ILP formulations for the semi-obnoxious p-median problem, a less-studied variant with practical relevance.

Findings

ReVelle & Swain's model performs best

Rosing et al.'s model is also highly effective

Experimental results validate the models' efficiency

Abstract

The p-median problem concerns the location of facilities so that the sum of distances between the demand points and their nearest facility is minimized. We study a variant of this classic location problem where minimum distance constraints exist both between the facilities and between the facilities and the demand points. This specific type of problem can be used to model situations where the facilities to be located are semi-obnoxious. But despite its relevance to real life scenarios, it has received little attention within the vast literature on location problems. We present twelve ILP models for this problem, coupling three formulations of the p-median problem with four formulations of the distance constraints. We utilize Gurobi Optimizer v9.0.3 in order to compare these ILP models on a large dataset of problems. Experimental results demonstrate that the classic p-median model proposed by ReVelle \& Swain and the model proposed by Rosing et al. are the best performers.