Joint optimization of train scheduling and rolling stock circulation planning with passenger flow control on tidal overcrowded metro lines

This study proposes a joint optimization method for train scheduling and rolling stock circulation planning with the consideration of passenger flow control strategy on a tidal oversaturated metro line, in which different types of rolling stocks with various loading capacities are put into operations to satisfy the uneven passenger demand in different periods (e.g., peak hours and off-peak hours). To characterize the problem mathematically, a mixed-integer nonlinear programming model is formulated to minimize the passenger waiting time and operating costs of the metro system simultaneously. This model is further reformulated equivalently into a mixed-integer linear programming model via the linearization method. An effective heuristic algorithm based on the tabu search and CPLEX solver is designed to find high-quality solutions for the proposed problem. Finally, two sets of numerical examples, including a small-scale example and a large-scale example based on the Beijing metro Batong line, are conducted to validate the performance of the proposed methods. The experimental results demonstrate that scheduling multiple types of rolling stocks can effectively reduce the transportation costs and satisfy passenger demand in different periods.