The flexible and real-time commute trip sharing problems

The Commute Trip Sharing Problem (CTSP) was introduced to remove parking pressure on cities, as well as corporate and university campuses. Its goal is to reduce the number of vehicles being used for daily commuting activities. Given a set of inbound and outbound requests, which consists of origin and destination pairs and their departure and return times, the CTSP assigns riders and a driver, as well as inbound and outbound routes, to each vehicle in order to satisfy time-window, capacity, and ride-duration constraints. The CTSP guarantees a ride back for each rider, which is a critical aspect of such a ride-sharing system. This paper generalizes the CTSP to account for uncertainties about the return trip. Each rider is assumed to have a return time specified by a distribution (learned from historical data) and, each day, a percentage of riders will want to preprone or postpone their return trip to accommodate some schedule changes. The paper proposes two generalizations of the CTSP: the Flexible CTSP (FCTSP) and the Real-Time CTSP (RT-CTSP). In the FCTSP, riders must confirm their final return times by a fixed deadline. In the RT-CTSP, riders confirm their new return times in real time with some prior notice. The paper proposes a two-step approach to address the FCTSP and the RT-CTSP. The first step uses a scenario-based stochastic program to choose the drivers and the morning routes in order to maximize the robustness of the driver assignment. The second step reoptimizes the plan at the fixed deadline or in real time once the return times are confirmed. Experiments on a real-world dataset of commute trips demonstrate the effectiveness of the algorithm in generating robust plans and reveal a trade-off between vehicle reduction and plan robustness as the robust plans tend to be conservative. A method is then proposed to evaluate this trade-off using the per-unit price ratio of vehicle increase to uncovered riders.