Robust maximum capture facility location under random utility maximization models

We study a robust version of the maximum capture facility location problem in competitive market, assuming that each customer chooses among all available facilities according to random utility maximization (RUM) model. employ generalized extreme value (GEV) family models and assume parameters RUM model are not given exactly but lie convex uncertainty sets. The is locate new maximize worst-case captured user demand. show that, interestingly, our preserves monotonicity submodularity from its deterministic counterpart, implying simple greedy heuristic can guarantee (1−1/e) approximation solution. further concavity objective function under classical multinomial logit (MNL) model, suggesting an outer-approximation algorithm be used solve MNL optimality. conduct experiments comparing method other sampling approaches, using instances different discrete choice models. Our results clearly demonstrate advantages protecting decision-maker scenarios.