Train unit routing problem determines the number of train units needed to carry out involved trips, which is a significant part of railway operation cost. In this paper, we focus on high-speed train unit routing problems, in which maintenance resource constraints both on time and distance are taken into account. Based on a connection network, this paper first proposes a general train unit routing model. Then, the general model is specialized to meet the circulation and maintenance conditions of high-speed train units in China, which is based on a special connection network with a two-day time horizon. A strategy is proposed to reduce the scale of the connection network, which improves the model's solvability. Furthermore, an extension on multi-depot train unit routing problem is discussed. Finally, numerical experiments based on the real data of Chinese high-speed railway are carried out to verify the effectiveness and efficiency of the proposed mode and method.@en

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.

@en