Combinatorial Aspects of Move - up Crews ⋆

Delays occurring during a crew’s duty may propagate to subsequent tasks, leading to cancelation of certain trains in the worst case. Instead of the original crew, a move-up crew may take over the rest of the delayed crew’s duty, which is then on time. In this paper, we address both the problem of how to create robust crew schedules yielding many of such move-up crews, as well as the problem of making optimal crew swap decisions during operations. We show how the first problem is related to a set cover variant with profits for pairs of sets and to densest k subgraph. We develop algorithms and complexity results for subproblems and show how to profit from these in heuristics for the original problem. For the second problem we give efficient algorithms for the local case and show that optimizing crew swaps over the whole railway network is NP-hard.