Ridesharing and fleet sizing for On-Demand Multimodal Transit Systems

This paper considers the design of On-Demand Multimodal Transit Systems (ODMTS) that combine fixed bus/rail routes between transit hubs with on-demand shuttles that serve the first/last miles to/from the hubs. The design problem aims at finding a network design for the fixed routes to allow a set of riders to travel from their origins to their destinations, while minimizing the sum of the travel costs, the bus operating costs, and rider travel times. The paper addresses two gaps in existing tools for designing ODMTS. First, it generalizes prior work by including ridesharing in the shuttle rides. Second, it proposes novel fleet-sizing algorithms for determining the number of shuttles needed to meet the performance metrics of the ODMTS design. Both contributions are based on Mixed-Integer Programs (MIP). For the ODMTS design, the MIP reasons about pickup and dropoff routes in order to capture ridesharing, grouping riders who travel to/from the same hub. The fleet-sizing optimization is modeled as a minimum flow problem with covering constraints. The natural formulation leads to a dense graph and computational issues, which is addressed by a reformulation that works on a sparse graph. The methodological contributions are evaluated on a real case study: the public transit system of the broader Ann Arbor and Ypsilanti region in Michigan. The results demonstrate the substantial potential of ridesharing for ODMTS, as costs are reduced by about 26% with respect to allowing only individual shuttle rides, at the expense of a minimal increase in transit times. Compared to the existing system, the designed ODMTS also cuts down costs by 35% and reduces transit times by 38%.