Train unit scheduling guided by historic capacity provisions and passenger count surveys

Train unit scheduling concerns the assignment of train unit vehicles to cover all the journeys in a fixed timetable. Coupling and decoupling activities are allowed in order to achieve optimal utilization while satisfying passenger demands. While the scheduling methods usually assume unique and well-defined train capacity requirements, in practice most UK train operators consider different levels of capacity provisions. Those capacity provisions are normally influenced by information such as passenger count surveys, historic provisions and absolute minimums required by the authorities. In this paper, we study the problem of train unit scheduling with bi-level capacity requirements and propose a new integer multicommodity flow model based on previous research. Computational experiments on real-world data show the effectiveness of our proposed methodology

On Integer Polytopes with Few Nonzero Vertices

We provide a simple description in terms of linear inequalities of the convex hull of the nonnegative integer vectors x that satisfy a given linear knapsack covering constrain