Andreas Bärmann , Alexander Martin , Jonasz Staszek
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引用次数: 0
摘要
在这项工作中,我们考虑的是铁路货运公司机车调度和司机分配的综合问题。我们的目标是计算出机车和司机对给定订单所列列车的最优同步分配。在数学上,这导致了一个带有兼容性约束的集合包装问题和一个多商品流问题的结合。我们开发了一种二元编程模型来模拟给定任务,并通过对原始的集合包装不等式进行基于类群的紧缩来改进该模型。该模型的目标函数确保尽可能多的列车运行。为了解决该问题的计算复杂性,我们引入了一种新颖的分解方法,将该问题分解为主机车调度问题和司机分配子问题。它利用了主问题比子问题更容易解决这一事实。对于主问题的任何固定解,我们都可以利用子问题来确认主问题解的可行性,或者从各种约束类别中推导出有效的不等式,以切断不可行的主问题解,并重新进行求解。为了进一步缩短求解时间,我们还开发了一种预解启发式。我们通过解决我们的行业合作伙伴 DB Cargo Polska S.A. 提供的一个大型实际问题实例以及一组衍生的现实实例,展示了所介绍方法的潜力。
A decomposition approach for integrated locomotive scheduling and driver assignment in rail freight transport
In this work, we consider the integrated problem of locomotive scheduling and driver assignment in rail freight companies. Our aim is to compute an optimal simultaneous assignment of locomotives and drivers to the trains listed in a given order-book. Mathematically, this leads to the combination of a set-packing problem with compatibility constraints and a multi-commodity-flow problem. We develop a binary-programming formulation to model the given task and improve it by performing a clique-based tightening of the original set-packing inequalities. The objective function of this model makes sure that as many trains as possible are running. To handle the computational complexity of the problem, we introduce a novel decomposition approach which decomposes the problem into a master locomotive scheduling problem and a subproblem for driver assignment. It exploits the fact that the master problem is empirically much easier to solve than the subproblem. For any fixed solution of the master problem, we can use the subproblem to either confirm feasibility of the master solution or to derive valid inequalities from various constraint classes to cut the infeasible master solution off and reiterate. To further improve solution times, we also develop a presolve heuristic. We demonstrate the potential of the presented method by solving a large-scale real-world problem instance provided by our industry partner DB Cargo Polska S.A., as well as a set of derived realistic instances.
期刊介绍:
The EURO Journal on Transportation and Logistics promotes the use of mathematics in general, and operations research in particular, in the context of transportation and logistics. It is a forum for the presentation of original mathematical models, methodologies and computational results, focussing on advanced applications in transportation and logistics. The journal publishes two types of document: (i) research articles and (ii) tutorials. A research article presents original methodological contributions to the field (e.g. new mathematical models, new algorithms, new simulation techniques). A tutorial provides an introduction to an advanced topic, designed to ease the use of the relevant methodology by researchers and practitioners.