Exploring Fairness in Train Timetabling and Rolling Stock Scheduling with Flexible (Un)coupling in a Y-Shaped Network

Abstract Flexible (un)coupling operation within a Y-shaped network allows for the dynamic adjustment of metro train formations at the diverging junction based on fluctuating passenger demand. Train timetable and rolling stock schedule serve as essential elements in organising efficient flexible (un)coupling train operation. However, reducing overall waiting time during the optimisation process may lead to disparities, where some passengers experience much longer waiting periods compared to others. To address this issue, we formulate a multi-objective optimisation model that jointly determines train formations, timetable, and rolling stock schedule while balancing operating cost, total waiting time, and fairness. Moreover, we design an operationalisation method for balancing the objectives and solve the problem using the Gurobi solver. Numerical experiments are conducted under different scenarios on a Y-shaped metro network in Guangzhou, China. The results reveal that the model can effectively improve fairness compared to cases without fairness considerations. By allowing a moderate increase in total waiting time or operating costs, passengers with the longest waiting times experience reduced waiting durations. The standard deviation of waiting times also decreases. For instance, a 25.6 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> rise in operating costs yields a 27.4 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> reduction in passenger waiting time cost and a 36.5 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>%</mml:mo> </mml:math> reduction in the standard deviation of waiting times. Ultimately, a more efficient balance between fairness, operating costs, and overall passenger waiting time is achieved.