**the maximum capture problem with flexible substitution patterns**at the 2016 Workshop on Discrete Choice Models hosted by the Transport and Mobility Laboratory, EPFL.

*Abstract*

We consider the maximum capture problem with random utilities. The basic assumption is that a firm wants to locate a given number of facilities in a competitive market where customers choose the facility that maximizes their utility. Utility is treated as random. In the location science literature so far, the corresponding choice probabilities of the customers are given by the multinomial logit model (MNL). There exist several exact mixed-integer linear reformulations to the original NP-hard, non-linear program. Unfortunately, the MNL exhibits the independence from irrelevant alternatives property, i.e., constant substitution between facility locations. In contrast, the so-called mixed multinomial logit model (MXL) allows for flexible substitution patterns. Moreover, the MXL is able to approximate any random utility model arbitrarily close. In this paper we present an intelligible mixed-integer linear program for the maximum capture problem with customer demand modeled by the MXL. Empirical and managerial insights are discussed based on a real world case study that shows the applicability of our approach.

**Keywords**: mixed logit model, multinomial logit model, random utility model, facility location, assortment optimization, product line planning, stochastic programming