Bilevel competitive facility location and design under a nested logit model

Abstract

This paper investigates a competitive facility location problem involving two companies entering a market. Both aim to locate and design new facilities to maximize revenue. The decision-making process involves one company acting as the “leader” making the initial decision, and the other as the “follower”, observing the leader’s decision before making its own. Customers choose between the two companies’ facilities based on a nested logit model (NLM). In our model, facilities are grouped into two categories to reflect similarities within each company’s facilities, resulting in a two-nest NLM. We aim to determine the optimal decision for the leader, considering the follower’s potential responses and customer preferences as dictated by the NLM. To solve this problem, we develop a nonlinear 0–1 bilevel program and propose an exact solution algorithm with two bounding problems and specialized branch-and-cut subroutines. The algorithm is guaranteed to converge to an optimal pessimistic bilevel solution in a finite number of iterations. Extensive computational experiments using a common testbed from existing literature validate our algorithm’s efficiency. Additionally, we conduct sensitivity analysis to examine the impact of NLM parameters on strategic location decisions and compare our NLM-based model with a multinomial logit model (MNL)-based model. Our findings show that using NLM over MNL can prevent potential revenue losses. Specifically, if the actual decision context is better represented by NLM but MNL is used by the leader, then the leader could face significant revenue decreases, up to 30.44%.