Store location with multipurpose shopping trips and a new random utility customers’ choice model

Abstract

This paper addresses retail store location in a duopoly. One firm, the so-called leader, has already located several stores, while a second firm, the follower that offers a different product, considers locating its stores in the same area. Both products have some degree of complementarity. Marianov et al. (2018) studied this problem considering a customer decision rule that is binary (winner-take-all) and deterministic (there are no uncertainties related to customers’ behavior). In that work, they concluded that multipurpose shopping has a strong influence on optimal store location. This paper extends that work by introducing random utility customer choice rules based on the Multinomial Logit model. Along these lines, we propose the new Partially Binary Logit rule, applicable to the case in which all stores of a firm have identical attributes, except for their location. In this case, a customer always chooses the least cost trip store of the firm to purchase its product. We propose one nonlinear and three linear formulations for the follower location problem, and a Branch and Cut method for one of them. Two of the formulations have a good performance for instances of up to at least 200 nodes. We compare the binary, Multinomial Logit, and Partially Binary Logit rules by analyzing the captured markets and location patterns for a large set of randomly generated 100-node instances.