Integer Linear Programming Models for Variations of the Discrete Semi-obnoxious Facility Location Problem

Abstract

In this work, we consider semi-obnoxious facility location problems, motivated by the following scenario: Suppose an international restaurant brand wants to open a chain of branches in a city that is already occupied by several competing brands. We model this as a geometric optimization problem to provide decision-makers with relevant information on how to economically place k new branches among competitors and how to set prices of items in comparison to nearby competitors. We refer to this as the discrete k-semi-obnoxious facility location (DSofl) problem, classifying it within the context of similar problems in the literature. We introduce two variations of the DSofl problem and propose integer linear programming (ilp) based exact methods for solving both. Additionally, we discuss the implementation of these models using the Gurobi solver. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.