A single-facility competitive location problem in the plane based on customer choice rules

Abstract

Since customer choice rules would greatly affect the performance of retail facilities, they should be considered when a chain wants to locate a new facility in a competitive market. In the existing studies, customers’ choice behavior is usually considered as homogeneous, which means that all customers patronize facilities with one kind of customer choice rules: the deterministic rule, the probabilistic rule or the multi-deterministic rule. However, it is not in line with reality as we have investigated people’s choice behavior on convenience stores by questionnaire surveys, and survey results show that different customers may patronize facilities with different choice rules. In order to study competitive facility location problems in which customers’ choice behavior is heterogeneous, we classify customers into three types by customer choice rules, the relative proportions of which are calculated based on questionnaires. A customer classification based competitive facility location model in the plane is proposed in which the location and quality of the new facility are to be determined in order to maximize the profit of the locating chain. Since the model is non-convex and discontinuous, and location problems are usually large-scale, four kinds of commonly used heuristic algorithms instead of exact algorithms are designed for obtaining a satisfactory solution including Particle Swarm Optimization, Tabu Search, Simulated Annealing and Genetic Algorithm. Numerical experiments show that Particle Swarm Optimization performs best both in computation efficiency and solution precision. Comparisons among location results employing different customer proportions reveal that customer proportion significantly affects location results. Most importantly, the locating chain may lose large profit once the customer proportion is wrongly estimated. Maximum profit loss is more than 20% in our cases.