  The performance of multimodal mobility systems relies on the seamless
integration of conventional mass transit services and the advent of
Mobility-on-Demand (MoD) services. Prior work is limited to individually
improving various transport networks' operations or linking a new mode to an
existing system. In this work, we attempt to solve transit network design and
pricing problems of multimodal mobility systems en masse. An operator (public
transit agency or private transit operator) determines the frequency settings
of the mass transit system, flows of the MoD service, and prices for each trip
to optimize the overall welfare. A primal-dual approach, inspired by the market
design literature, yields a compact mixed integer linear programming (MILP)
formulation. However, a key computational challenge remains in allocating an
exponential number of hybrid modes accessible to travelers. We provide a
tractable solution approach through a decomposition scheme and approximation
algorithm that accelerates the computation and enables optimization of
large-scale problem instances. Using a case study in Nashville, Tennessee, we
demonstrate the value of the proposed model. We also show that our algorithm
reduces the average runtime by 60\% compared to advanced MILP solvers. This
result seeks to establish a generic and simple-to-implement way of revamping
and redesigning regional mobility systems in order to meet the increase in
travel demand and integrate traditional fixed-line mass transit systems with
new demand-responsive services.
