  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, non-convex 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 combining tailored 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,
while 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 outcomes for
both types of operators, thus incentivizing profit-oriented MOD operators to
adopt transit priorities.
