Bilevel subsidy-enabled mobility hub network design with perturbed utility coalitional choice-based assignment

Urban mobility is undergoing rapid transformation with the emergence of new services. Mobility hubs (MHs) have been proposed as physical-digital convergence points, offering a range of public and private mobility options in close proximity. By supporting Mobility-as-a-Service, these hubs can serve as focal points where travel decisions intersect with operator strategies. We develop a bilevel MH platform design model that treats MHs as control levers. The upper level (platform) maximizes revenue or flow by setting OD based pricing to travelers and subsidies to incentivize last-mile operators. The lower level captures joint traveler-operator decisions with a link-based Perturbed Utility Route Choice (PURC) assignment, yielding a strictly convex quadratic program. We reformulate the bilevel problem to a single-level program via the KKT conditions of the lower level and solve it with a gap-penalty method and an iterative warm-start scheme that exploits the computationally cheap lower-level problem. Numerical experiments on a toy network and a Long Island Rail Road (LIRR) case (380 nodes, 642 links, 78 ODs) show that the method attains sub-1% optimality gaps in less than 30 min. In the base LIRR case, the model allows policymakers to set the optimal platform access fee and operator subsidy. We then evaluate the impact of operator competition, quantify the social surplus value of a MH, and how restrictive subsidy can discourage operator participation.