In almost all Japanese railway companies, rolling stock management still relies on manual procedure. As density of trains and interconnectivity between lines are increased, a support system for the management gets to be important. This paper focuses on a scheduling task for vehicle units' operation and a support system for rescheduling vehicle units' operation in train service disruption. A schedule of vehicle units' operation is modified by a dispatcher to keep consistency between train timetable and vehicle unit assignment. When there is no solution, the dispatcher has to ask a train service manager to change train timetable. To support this task, we developed an algorithm of rescheduling vehicle unit operation, which included relaxation of constraints. Our algorithm represents constraints as a network model, and, if necessary, relaxes constraints by modifying the network model during search of a solution. This paper indicates the network model, the algorithm of searching for a solution as relaxing constraints, and numerical experiments using a real middle-size data. The results of the experiments showed that our algorithm could calculate various solutions with relaxed constraints. Analyzing the solutions at the viewpoints of train service and rolling stock operation, we showed the effectiveness of a system that proposes various solutions using our algorithm. C⃝ 2018 Wiley Periodicals, Inc. Electr Eng Jpn, 203(4): 31-44, 2018; Published online in Wiley Online Library (wileyonlinelibrary.com).

We propose a method for solving the crew rescheduling problem (CRP) and the vehicle rescheduling problem (VRP) based on the Lagrangian relaxation method. The CRP/VRP is formulated as an integer programming problem on the basis of a network flow modeling approach from which a Lagrangian relaxation problem is constructed by relaxing the constraint that links multiple resources. Using two procedures that generate the upper and lower bounds of the primal problem, both of which utilize an efficient shortest path algorithm for the directed acyclic graph (DAG), the proposed method gradually improves the gap between the upper and lower bounds while updating Lagrangian multipliers. Experimental results of real-world vehicle rescheduling data from Japanese railway lines indicated that the proposed method generated feasible solutions that were confirmed to be fairly close to the optimal solutions according to the gap between the upper and lower bounds, and also clarified the quality of the other method's solution by using the gap, which could lead to streamlining and sophisticating real-world rescheduling related activities.

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