Multimodal Transportation Pricing Alliance Design: Large-Scale Optimization for Rapid Gains

Transit agencies have the opportunity to outsource certain services to established mobility-on-demand (MOD) providers. Such alliances can improve service quality, coverage, and ridership; reduce public sector costs and vehicular emissions; and integrate the passenger experience. To amplify the effectiveness of such alliances, we develop a fare-setting model that jointly optimizes fares and discounts across a multimodal network. We capture commuters’ travel decisions with a discrete choice model, resulting in a large-scale, mixed-integer, nonconvex optimization problem. To solve this challenging problem, we develop a two-stage decomposition with the pricing decisions in the first stage and a mixed-integer linear optimization of fare discounts and passengers’ travel decisions in the second stage. To solve the decomposition, we develop a new solution approach that combines customized coordinate descent, parsimonious second-stage evaluations, and interpolations using special ordered sets. This approach, enhanced by acceleration techniques based on slanted traversal, randomization, and warm-start, significantly outperforms algorithmic benchmarks. Different alliance priorities result in qualitatively different fare designs: flat fares decrease the total vehicle-miles traveled, whereas geographically informed discounts improve passenger happiness. The model responds appropriately to equity-oriented and passenger-centric priorities, improving system utilization and lowering prices for low-income and long-distance commuters. Our profit allocation mechanism improves the outcomes for both types of operators, thus incentivizing profit-oriented MOD operators to adopt transit priorities.