Incorporating reservation strategies into demand management and train scheduling in metro systems

Abstract

Emerging reservation-based travel technologies offer a promising solution to mitigate supply-demand mismatches in metro systems. This paper presents a framework to support metro operators by optimizing time-varying reservation slot allocation plans, passenger flow control strategies, and train schedules. The proposed approach ensures that passengers with reservations can directly access platforms and board the first available train services, while those without reservations are managed through effective passenger flow control strategies to optimize train capacity utilization. To address this, an integer nonlinear programming model is formulated, incorporating constraints that capture interactions between passengers with and without reservations, with the objective of minimizing passengers’ waiting time and line congestion. A hybrid algorithm is developed to improve computational efficiency, combining the adaptive large neighborhood search method with a commercial solver and incorporating valid inequalities tailored to the properties of the model. The effectiveness of the proposed approaches is demonstrated through numerical experiments using real-world operational data from the Beijing metro Batong line. Computational results indicate that the integrated optimization approach reduces the objective value by 6.19 % compared to a step-by-step optimization method, achieving better alignment of capacity with dynamic passenger flows. In addition, the extreme unfairness between reserved and unreserved passengers, where passengers with reservations have a 100 % service ratio compared to less than 20 % for unreserved passengers, is mitigated by increasing passenger waiting times by 3.51 % and line congestion by 0.51 %. Furthermore, the proposed algorithm efficiently solves large-scale and real-world instances, outperforming the state-of-the-art commercial solver.