Efficient asymmetric reposition strategy of rolling stock for urban rail transit systems

Balancing energy efficiency with high-quality service on urban rail lines with highly asymmetric passenger demand is a crucial yet challenging issue. This paper proposes an efficient asymmetric rolling stock reposition strategy to simultaneously optimize the train timetable, speed profiles and rolling stock circulation, given the passenger demand in the undersaturated direction and timetable in the oversaturated direction. By constructing space-time networks for passengers and rolling stocks, respectively, an integer linear programming model is formulated by considering the tradeoff between the passenger travel time and train energy cost. A rolling horizon scheme incorporating the Lagrangian relaxation decomposition technique is designed, which can be decomposed into two subproblems by relaxing the capacity constraints. The effectiveness of our proposed methodology is validated through numerical experiments on a test network and the Beijing Batong Line, demonstrating that the optimized train circulation plan significantly reduces energy consumption while incurring a minimal increase in travel time.