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Subway lines connecting different urban functional zones in large cities have directiondependent and time-variant passenger demand, namely, asymmetry in passenger demand. Most existing studies adopt a symmetric strategy to design operations in both directions and sequentially optimize the different problems associated with operations, thereby failing to meet the asymmetry in passenger demand. This study formulates an asymmetric operation strategy as an integrated mixed-integer non-linear model to optimize the entire operational process of rolling stock from the perspective of service quality and operating costs. Based on the proposed model, an exact algorithm is proposed with speed-up techniques to quickly generate an optimal solution. To this end, the original model is decomposed into several sub-problems that can be exactly solved by using a forward dynamic programming algorithm. Based on actual data from the Beijing subway's Yizhuang line, numerical experiments are conducted to investigate the effectiveness of the asymmetric operation strategy, to identify managerial insights on the integrated optimization, and to evaluate the performance of the proposed methodology.

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