  This paper considers facility location problems in which a firm entering a
market seeks to open facilities on a subset of candidate locations so as to
maximize its expected market share, assuming that customers choose the
available alternative that maximizes a random utility function. We introduce a
deterministic equivalent reformulation of this stochastic problem as a maximum
covering location problem with an exponential number of demand points, each of
which is covered by a different set of candidate locations. Estimating the
prevalence of these preference profiles through simulation generalizes a sample
average approximation method from the literature and results in a maximum
covering location problem of manageable size. To solve it, we develop a partial
Benders reformulation in which the contribution to the objective of the least
influential preference profiles is aggregated and bounded by submodular cuts.
This set of profiles is selected by a knee detection method that seeks to
identify the best tradeoff between the fraction of the demand that is retained
in the master problem and the size of the model. We develop a theoretical
analysis of our approach and show that the solution quality it provides for the
original stochastic problem, its computational performance, and the automatic
profile-retention strategy it exploits are directly connected to the entropy of
the preference profiles in the population. Computational experiments indicate
that our approach dominates the classical sample average approximation method
on large instances, can outperform the best heuristic method from the
literature under the multinomial logit model, and achieves state-of-the-art
results under the mixed multinomial logit model. We characterize a broader
class of problems, which includes assortment optimization, to which the solving
methodology and the analyses developed in this paper can be extended.
