Locating Facilities under Competition and Market Expansion: Formulation, Optimization, and Implications

Abstract

As the ongoing battle between brick-and-mortar stores and e-commerce shops escalates, managers of the former are becoming more cautious regarding their strategic store site selection and decoration decisions, particularly if foreseeable competition from rival companies exists. This article investigates a bilevel competitive facility location problem (BCFL), where two companies, a leader and a follower, plan to enter a market sequentially. Each company has a budget to open and design facilities. The goal is to maximize expected revenue that is forecasted through a discrete choice model. To reflect a practical environment, we further consider a situation with elastic demand, explaining the market expansion effect when customers are offered better service due to open new facilities. We formulate the problem as a nonlinear 0-1 bilevel program. Because of the bilevel structure and the market expansion effect, this problem is such challenging that we are unaware of any exact algorithms in the literature. Motivated by this gap, we develop an exact framework that leverages the state-of-the-art value-function-based approach. However, this framework requires solving a mixed-integer non-convex optimization problem (MINOP) at each iteration, which is computationally prohibitive even for medium-scale instances. To mitigate the intractability, we propose a new framework that avoids MINOP and tackles instances with hundreds of location variables. Finally, we conduct extensive computational studies to show the efficiency and effectiveness of our method as well as provide insightful guidance for managers to have win-win/dominate outcomes and choose an appropriate market size function when dealing with expansion decisions in chained business operations.