Revisiting Stackelberg p-median problem with user preferences

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 facility choices. The problem can be visualized as a leader-follower game in which the operator is the leader who 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 open facility. 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 discuss various exact branch-and-cut solution approaches. In particular, we develop two approaches that have not been applied to PUP thus far. The first one explores the bilevel structure of the problem and derives an effective bilevel feasibility cut, whereas the second one is based on Benders decomposition, which is further accelerated using analytical Benders separation and heuristic separation. Using a broad testbed and benchmarks, we demonstrate the efficiency of our algorithms. Finally, we conduct sensitivity analysis to draw additional implications and to highlight the importance of considering user preferences when they exist.