Discrete location planning

Two new models for discrete location planning under static competition are introduced. The empirical context is an enterprise that is planning to set up a number of stores in various locations. The probability that a customer chooses a specific store is obtained from a multinomial logit (MNL) model. In the first model we apply the basic MNL model where the choice set contains all potential locations. To obtain the choice probabilities of a reduced choice set, we take advantage of the property of constant substitution patterns which can be modelled by linear constraints. In the second model we consider the case where flexible substitution patterns are accounted for. The main idea is to simulate, for a given number of individuals, their alternative specific utility values. Thus for each individual, we can identify which locations have to be opened to attract an individual as a customer. We consider two parcel service providers in the City of Dresden. Both approaches can be solved very fast within few minutes with a small solution gap by a state-of-the-art solver