Aggregation formulation for on-site multidepot vehicle scheduling scenario

The multidepot vehicle scheduling problem (MDVSP) is a fundamental public transport challenge. To address the large-scale model and inherent solution symmetry associated with the traditional trip-to-trip connection-based approach for MDVSP, a new trip-to-route (T2R) connection-based approach is proposed. Considering real-world problem characteristics with numerous trips sharing common origin–destination stations and travel times on one route, this approach aggregates same vehicle possible trip sequences into a T2R connection. Two time-space network aggregation (TSNA) flow formulation versions, route pair-based TSNA and station pair-based TSNA, were constructed. Furthermore, TSNA equivalence under any given decomposition strategy, including first-in-first-out, with the multicommodity network flow (MCNF) model was demonstrated. Given the favorable separable TSNA structure, an alternating direction method of multipliers (ADMM)-based procedure is proposed to decompose the MDVSP into multiple subproblems that can be linearized and readily solved using commercial solvers. The quality of the solutions was assessed using lower bounds obtained from the Lagrangian relaxation problem. The effectiveness and superiority of the proposed MDVSP models and algorithms were subsequently confirmed using random data sets and real-world instances.