Rolling stock needs regular maintenance in a maintenance facility. Rolling stock from different fleets are routed to maintenance facilities by interchanging the destinations of trains at common stations and by using empty drives. We consider the problem of locating maintenance facilities in a railway network under uncertain or changing line planning, fleet planning and other uncertain factors. These uncertainties and changes are modeled by a discrete set of scenarios. We show that this new problem is NP-hard and provide a two-stage stochastic programming and a two-stage robust optimization formulation. The second-stage decision is a maintenance routing problem with similarity to a minimum cost-flow problem. We prove that the facility location decisions remain unchanged under a simplified routing problem and this gives rise to an efficient mixed integer programming (MIP) formulation. This result also allows us to find an efficient decomposition algorithm for the robust formulation based on scenario addition (SA). Computational work shows that our improved MIP formulation can efficiently solve instances of industrial size. SA improves the computational time for the robust formulation even further and can handle larger instances due to more efficient memory usage. Finally, we apply our algorithms on practical instances of the Netherlands Railways and give managerial insights.

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Real-life planning problems are often complicated by the occurrence of disturbances, which imply that the original plan cannot be followed anymore and some recovery action must be taken to cope with the disturbance. In such a situation it is worthwhile to arm yourself against possible disturbances by including recourse actions in your planning strategy. Well-known approaches to create plans that take possible, common disturbances into account are robust optimization and stochastic programming. More recently, another approach has been developed that combines the best of these two: recoverable robustness. In this paper, we solve recoverable robust optimization problems by the technique of column generation. We consider two types of decomposition approaches: separate recovery and combined recovery. We investigate our approach for two example problems: the size robust knapsack problem, in which the knapsack size may get reduced, and the demand robust shortest path problem, in which the sink is uncertain and the cost of edges may increase. For each problem, we present elaborate computational experiments. We think that our approach is very promising and can be generalized to many other problems.

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