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As the core of the rail freight flow organization process, train formation problem (TFP) has attracted much attention. In Chinese practice, car flow routing, TFP, and train routing are usually optimized sequentially to reduce the complexity of computation, which may result in a local optimum, and even no feasible solution. To address this issue, this paper studies the integrated optimization of the three sub problems with aims to minimize the total cost of transportation cost, accumulation cost, and classification cost. An integer linear arc-based model incorporating the unitary and in-tree rules of a shipment is first formulated and solved by the state-of-the-art solver GUROBI. Since GUROBI can’t deal with the large test cases, a path-based model is built and solved by a bespoken two-phase algorithm. The first phase of the algorithm is Benders-and-Price approach that combines Benders decomposition and column generation, and the second phase is to solve the arc-based model with some variables fixed as the corresponding values fetched from the first phase. The results show that the proposed algorithm outperforms GUROBI, and the acceleration techniques, i.e., trust region and Pareto-optimal cuts, can improve the convergence efficiency of Benders decomposition significantly.

Optimizing Train Formation Problem With Car Flow Routing and Train Routing by Benders-and-Price Approach