Integrated Train Timetabling and Rolling Stock Scheduling Model Based on Time-Dependent Demand for Urban Rail Transit

The congestion of urban transportation is becoming an increasingly critical problem for many metropolises. The Urban Rail Transit (URT) system has attracted substantial attention due to its safety, high speed, high capacity, and sustainability. With a focus on a holistic modeling framework for train scheduling problems, this article proposes a novel optimization methodology that integrates both train timetabling and rolling stock scheduling based on time-dependent passenger flow demands. We particularly consider the tradeoff between waiting times for passengers and the train frequency of the URT system. By using train paths and rolling stock indicators as decision variables, this problem is formulated as a bi-level programming model. A simulated-annealing (SA)-based heuristic algorithm is employed to solve the proposed model and generate approximate optimal solutions. In the case study of Line 10 of Beijing Subway, GAMS (The General Algebraic Modeling System) with the IBM ILOG CPLEX Optimization Studio (CPLEX) solver can barely obtain a solution in more than 2 hours, whereas the SA-based heuristic can obtain the solution within 16 minutes and 44 seconds with the objective value improved by more than 14%. The calculation results and comparisons indicate that the SA-based heuristic can efficiently produce approximate optimal scheduling strategies; these findings demonstrate the practical value of our proposed approaches.