Combining state-of-the-art row generation methods for the competitive facility location problem with multinomial logit choice rule

Abstract

The competitive facility location problem, in which customers are assumed to use the multinomial logit rule to choose where to purchase, has gained increasing attention in the location field. In 2014, a comparison between the most successful exact solution methods at that time was published. These were based on the linearization of the logit formula. In the ten years following that comparison, important advancements have been made in finding exact solutions to the problem based on row generation methods. Different types of cuts have been proposed together with two approaches of using them. We introduce the three articles that represent the state-of-the-art, and we combine the cuts and methods presented in these articles to explore new approaches and find the best exact methods using an empirical approach to the most popular test instances. The best methods obtained have not been presented in the literature so far. We also discuss some improvement paths.