A continuum perspective of customer choice rules for competitive facility location problems

Abstract

Customer patronage behavior plays a critical role in estimating market share in the context of locating competitive facilities. Three common rules used to describe customer patronage behaviors are: the binary rule, the proportional rule, and the partially binary rule. Recently, we propose another customer choice rule, the partially proportional rule, to describe the behavior of customers when choosing a chain of facilities that offer exclusive services. Although these four rules describe very different customer patronage behaviors, this paper finds that they actually correspond to optimal solutions for four special cases of a class of optimization problems. For the general cases of this class of optimization problems, we also give the corresponding optimal solutions. This work provides a continuum perspective for understanding customer choice rules, while providing possible theoretical guidance for studying unexplored customer behavior patterns.