Optimizing Modular Vehicle Public Transportation Services with Short-Turning Strategy and Decoupling/Coupling Operations

In public transportation systems, the passenger demand during peak hours is characterized by over-saturation at intermediate stops and directional imbalances, and the traditional single scheduling strategy and fixed capacity cannot solve the contradiction between the demand and capacity mismatch. In order to accurately match demand and capacity, this paper proposes a method to optimize the service of a public transportation system by using a short-turning strategy combined with decoupled/coupled operation of modular vehicles (MVs). The short-turning strategy is used to alleviate the heavy passenger flow at intermediate stations, and the decoupling/coupling operations of MVs are employed to flexibly adjust the capacity levels in different directions. Considering urban space limitations, depots for storing modular units (MUs) are only set up at the starting and ending stations of bidirectional lines. MVs can not only adjust the departure capacity at the starting station but also consider whether to decouple/couple at turnaround stations for short-turning trips to achieve a more effective supply–demand match, with the decoupled/coupled MUs being deadheaded from or provided by the depot. We formulated this problem as an integer nonlinear programming (INLP) model, jointly optimizing the departure intervals of each trip, the capacity of MVs, the turnaround scheme for short-turning trips, and the decoupling/coupling scheme for MVs at turnaround stations, with the aim of minimizing passenger waiting time costs and vehicle operating costs. To facilitate a solution, we equivalently transformed some nonlinear terms in the model, which was then solved by the commercial solver Gurobi. The numerical study shows that, compared with the traditional full-length strategy combined with conventional buses, the model proposed in this paper can reduce the total system cost by about 19.59%. In particular, it can achieve precise matching between passenger demand and transport capacity, thereby reducing the passenger waiting time cost by about 29.99%. Compared with the full-length strategy combined with MVs, the total system cost is also reduced by about 14.65%. The research results contribute to enhancing the service quality and efficiency of public transportation systems, which is of great significance to the sustainable development of these systems.