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Traditionally, two variants of the L-shaped method based on Benders’ decomposition principle are used to solve two-stage stochastic programming problems: the single-cut and the multi-cut version. The concept of an oracle with on-demand accuracy was originally proposed in the context of bundle methods for unconstrained convex optimzation to provide(More)
The Vehicle Scheduling Problem (VSP) is the task of building an optimal set of rotations (vehicle schedule), such that each trip of a given timetable is covered by exactly one rotation. The restrictions and optimization criteria may differ from one problem setting to another. For multi-depot, multi-vehicle-type VSP for bus transit, each one-day rotation(More)
We discuss timetables in ex-urban bus traffic that consist of many trips serviced every day together with some exceptions that do not repeat daily. Traditional optimization methods for vehicle and crew scheduling in such cases usually produce schedules that contain irregularities which are not desirable especially from the point of view of the bus drivers.(More)