Anticipatory demand planning for microtransit with strategic use of latent capacity at fixed stops

Microtransit systems that integrate both advance reservations and on-demand requests offer a promising solution to combine the reliability of fixed-route transit with the flexibility of dynamic ride-sharing. The efficient operation of such hybrid systems requires careful coordination between the reservation and online phases. However, existing research mainly focuses on online adaptation, neglecting the potential of the reservation stage to shape more stable and efficient operations. In this study, we propose an efficient microtransit framework that leverages reservation-stage flexibility to cushion demand variability during real-time adaptation. We formulate the reservation-stage problem as a Chance-Constrained Dial-a-Ride Problem with Soft Time Windows (CCDARP-STW), which captures two key aspects: (i) temporal flexibility through user-specified acceptable arrival windows during reservations, and (ii) anticipatory capacity margins estimated via chance-constrained optimization based on a Poisson process model to reflect expected online demand. To solve CCDARP-STW efficiently, we develop a tailored Branch-and-Cut-and-Price (BCP) algorithm that incorporates a novel probabilistic dominance rule. Our experiments on the Cordeau DARP benchmark show that the proposed BCP algorithm maintains optimality while reducing runtime by about one-third on average, with even greater savings for more complex instances. Using a real-world case study based on Birmingham, Alabama, paratransit data, we further demonstrate that the anticipatory reservation-stage framework combined with rolling-horizon adaptation consistently improves request fulfillment and lowers adjustment costs per served request, enhancing service reliability under demand variability. Sensitivity analyses on hyperparameters, demand distribution deviation, and objective-weight selection highlight the trade-offs among reliability, efficiency, and flexibility, offering practical guidance for scaling hybrid microtransit systems in dynamic environments.