Integrated Optimization Method for Cross-Line Operations of Subway Crew Scheduling

This study addresses the collaborative optimization of crew scheduling and rostering for subway trains operating in a cross-line pattern. It investigates the impact of an integrated optimization approach, based on a cyclic roster system, on both the efficiency of crew plan formulation and the utilization rate of crew members. A spatiotemporal network is constructed based on the cyclic roster system to search for feasible crew duty segments and the sequence of shift connections within a roster cycle. A mathematical model is formulated with the dual objectives of minimizing the total number of crew shifts and minimizing idle time during duties. Constraints are established, including crew shift connection rules and shift feasibility requirements, to define permissible roster paths for crew members. These constraints ensure that the assigned duties within the roster cycle comply with the rules for connecting duty segments. A roster path search algorithm and an improved column generation algorithm are developed, considering factors such as sign-on/sign-off depots for shifts, shift types, roster cycle length, and the shift system design. These algorithms are employed to obtain optimal duty assignments within the roster cycle. Furthermore, a hybrid roster system is proposed, exploring the effects of mixing "four crews for three operational shifts" and "six crews for five operational shifts" systems on the crew schedule. The results show that, compared to the traditional separate "four crews for three shifts" and "six crews for five shifts" systems, the proposed hybrid system within the integrated optimization framework increases the average shift efficiency by 1.5 and 2.3 percentage points, respectively. It also reduces the number of deadhead segments by 12.18% and 24.45%, respectively. Compared to a sequential (two-stage) optimization approach, the integrated method improves average shift efficiency and crew utilization rate without increasing the number of shifts worked per crew member. Additionally, it reduces the total number of shifts required within the roster cycle and decreases the redundancy in covering duty segments. The integrated optimization approach with the hybrid roster system can adapt to flexibile roster cycles and the spatio-temporal distribution differences of duty segments across various lines. This adaptability is beneficial for ensuring balanced duty assignments for crew members and enhancing their overall utilization efficiency.