The follower competitive facility location problem under the nested logit choice rule

Recently, more realistic customer choice rules based on the Multinomial Logit have been proposed for the follower competitive facility location problem, together with efficient exact solution methods based on cut generation approaches. We address this problem in the case in which a new chain, the entrant, decides to locate some stores in a market where there are already incumbent chains offering substitute products, which differ from the entrant's product in secondary features. The entrant's stores are very similar to each other, and this is also the case for the incumbent chains. In this case, for a given customer, purchases made at the stores of one of the chains are correlated, given the similitude between these stores. The Multinomial Logit rule does not capture this correlation. We propose using a Nested Logit rule which does capture this correlation and, in addition, represents a sequential decision process by the customer, who first chooses the chain and then the store. We prove the concavity of the objective function in the problem and find exact solutions using Branch and Cut over a generalized linear reformulation of the problem and four different types of cuts: submodular and an improvement of these, outer-approximation, and a set of new cuts. Our results show locations that fit better the intuition and practice. Furthermore, our computational times improve in many cases upon the known results for similar problems.