Decomposition approach for Stackelberg P-median problem with user preferences

TL;DR

This paper introduces an efficient exact branch-and-cut decomposition algorithm for the P-median problem with user preferences, significantly improving solution times for large-scale instances and emphasizing the importance of user preferences.

Contribution

The paper develops a novel exact algorithm with acceleration techniques for the PUP, outperforming existing methods and enabling large-scale problem solving.

Findings

Algorithm outperforms existing approaches by orders of magnitude in computational time.

Effective decomposition and acceleration techniques enhance large-scale problem solving.

Sensitivity analysis highlights the impact of user preferences on facility location decisions.

Abstract

The P-median facility location problem with user preferences (PUP) studies an operator that locates P facilities to serve customers/users in a cost-efficient manner, upon anticipating customer preferences and choices. The problem can be visualized as a leader-follower game in which the operator is the leader that opens facilities, whereas the customer is the follower who observes the operator's location decision at first and then seeks services from the most preferred facility. Such a modeling perspective is of practical importance as we have witnessed its applications to various problems, such as the establishment of power plants in energy markets and the location of healthcare service centers for COVID-19 Vaccination. Despite that a considerable number of solution methodologies have been proposed, many of them are heuristic methods whose solution quality cannot be easily verified. Moreover, due to the hardness of the problems, existing exact approaches have limited performance. Motivated by these observations, we aim to develop an efficient exact algorithm for solving large-scale PUP models. We first propose a branch-and-cut decomposition algorithm and then design accelerated techniques to further enhance the performance. Using a broad testbed, we show that our algorithm outperforms various exact approaches by a large margin, and the advantage can go up to several orders of magnitude in terms of computational time in some datasets. Finally, we conduct sensitivity analysis to draw additional implications and to highlight the importance of considering user preferences when they exist.