Rolling stock rescheduling in high-speed railway networks via a nested Benders decomposition approach

Abstract

This paper addresses a rolling stock rescheduling problem (RSRP) during disruptions in a high-speed railway network, focusing on decisions related to the reassignment of physical rolling stock units to trips, deadheading schedules, and maintenance plans and schedules, while taking into account deadheading trips and maintenance requirements. A mixed integer linear programming (MILP) model is formulated, leveraging a directed acyclic graph to represent all feasible connections for each rolling stock unit. The objective is to minimize the weighted sum of canceled trips, schedule deviations, and various service quality and cost indicators. An exact nested Benders decomposition (NBD) algorithm is developed to solve this model. In the algorithm, the RSRP is first decomposed into an outer integer master problem (OMP) and an outer integer subproblem (OSP). The OMP is then divided into an inner integer master problem (IMP) and an inner integer subproblem (ISP), and is solved using the logic-based Benders decomposition (LBBD) algorithm, where strengthened feasibility cuts and optimality cuts, as well as valid inequalities, are added to the IMP to enhance the algorithm’s performance. The OSP, a feasibility problem, is further decomposed into many easier problems at each depot. Subsequently, three implementations including two branch-and-check type approaches and one LBBD approach are customized to solve the outer decomposition problem. We also propose a three-stage approach to solve the IMP, ISP, and OSP, sequentially. The approaches are tested on a set of instances constructed from the high-speed railway network in China. The results show that the approaches can quickly find (near-)optimal solutions for tested instances within a short computation time of several minutes, making it suitable for real-time rolling stock rescheduling applications.