Submodularity and local search approaches for maximum capture problems under generalized extreme value models

We study the maximum capture problem in facility location under random utility models, i.e., of seeking to locate new facilities a competitive market such that captured user demand is maximized, assuming each customer chooses among all available according maximization model. employ generalized extreme value (GEV) family discrete choice models and show objective function this context monotonic submodular. This finding implies simple greedy heuristic can always guarantee (1−1/e) approximation solution. further develop algorithm combining heuristic, gradient-based local search, an exchanging procedure efficiently solve problem. conduct experiments using instances different sizes we our approach significantly outperforms prior approaches terms both returned CPU time. Our theoretical findings be applied problems various literature, including popular multinomial logit, nested cross mixed logit models.