Discrete optimization in public rail transport
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
A branch-first, cut-second approach for locomotive assignment
Management Science
A Survey of Optimization Models for Train Routing and Scheduling
Transportation Science
Simultaneous Assignment of Locomotives and Cars to Passenger Trains
Operations Research
Journal of Global Optimization
Allocation of Railway Rolling Stock for Passenger Trains
Transportation Science
Efficient Circulation of Railway Rolling Stock
Transportation Science
Circulation of railway rolling stock: a branch-and-price approach
Computers and Operations Research
Solving a real-world train-unit assignment problem
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
Railway Rolling Stock Planning: Robustness Against Large Disruptions
Transportation Science
A Lagrangian heuristic for a train-unit assignment problem
Discrete Applied Mathematics
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Passenger railway systems are highly complex systems requiring the solution of several planning problems that can be analyzed and solved through the application of mathematical models and optimization techniques, which generally lead to an improvement in the performance of the system, and also to a reduction in the time required for solving these problems. The planning process is generally divided into several phases: Line Planning, Train Timetabling, Train Platforming, Rolling Stock Circulation and Crew Planning. In this paper, the Train-Unit Assignment Problem (TUAP), an important NP-hard problem arising in the Rolling Stock Circulation phase, is considered. In TUAP, we are given a set of timetabled trips, each with a required number of passenger seats, and a set of different train units, each having a cost and consisting of a self-contained train with an engine and a set of wagons with a given number of available seats. TUAP calls for the minimum cost assignment of the train units to the trips, possibly combining more than one train unit for a given trip, so as to fulfill the seat requests. Two Integer Linear Programming (ILP) formulations of TUAP are presented together with their relaxations. One is the Linear Programming (LP) relaxation of the model and valid inequalities are introduced for strengthening it. The other is based on the Lagrangian approach. Constructive heuristic algorithms, based on the previously considered relaxations, are proposed, and their solutions are improved by applying local search procedures. Extensive computational results on real-world instances are reported, showing the effectiveness of the proposed bounding procedures and heuristic algorithms.