Optimization of periodic crew schedules with application of column generation method

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, place - europe, operations - scheduling, organisation - workforce planning


Railway service plan, Train scheduling, Crew scheduling, Periodic schedule, Frame concept, Column generation


We present an alternative approach to the problem of periodic crew scheduling. We introduce the concept of frames which leads us to a modeling approach which suits well the current practice of the majority of European railway operators. It results in a model facilitating column generation techniques resulting in a Dantzig-Wolfe type decomposition, and thus suitable for a parallel implementation in a high-performance computing environment. We exploit the properties of network flow models to avoid several additional integer constraints. We compare two approaches to solve the problem. The first approach consists of solving the original problem by single model. The second approach is our step-by-step column generation. The comparison is based on our implementation which we describe in detail along with its application to certain benchmark instances. The benchmarks originate in real or close-to-realistic problems from railway systems in Slovakia and Hungary. The case studies demonstrate that our model is well-suited for real-life applications.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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