Real-time demand-responsive transit service design: A future-aware itinerary-based framework

This paper studies a real-time demand-responsive transit (DRT) system in which the operator presents each incoming request with a small menu of feasible service options, each specified by an explicit itinerary and a corresponding price. This setting gives rise to a future-aware service-offer design problem, because each offered option must be evaluated not only by its attractiveness to the current passenger, but also by its effect on future system operations. Unlike freight-delivery settings, where customers typically choose among abstract service-time promises, real-time DRT requires the itinerary itself to be designed as part of the offered service product. We formulate this problem as an event-based Markov decision process (MDP) and develop a three-stage modeling framework that sequentially determines feasible physical trip arrangements, service promises, and the displayed itinerary menu with prices. We establish that, for any given continuation-value function, the three-stage framework exactly solves the corresponding one-step lookahead optimization of the MDP. Since the exact continuation value is generally unavailable, we approximate the post-decision value function using a simulation-based neural network and derive a bound on the resulting policy loss relative to the exact MDP solution. Numerical experiments show that the proposed framework outperforms benchmark policies, while feature-ablation and runtime tests support the effectiveness of the proposed state representation and its applicability to real-time operation. The results also provide insights into the roles of transfer, supply conditions, and demand–supply imbalance in real-time passenger transportation.