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**A branch and bound algorithm for scheduling trains in a railway network.**
*(English)*
Zbl 1179.90135

Summary: The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits.

### MSC:

90B35 | Deterministic scheduling theory in operations research |

90C57 | Polyhedral combinatorics, branch-and-bound, branch-and-cut |

### Keywords:

train scheduling; real-time conflict resolution; alternative graph; branch and bound algorithm
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\textit{A. D'ariano} et al., Eur. J. Oper. Res. 183, No. 2, 643--657 (2007; Zbl 1179.90135)

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