Reducing the Adaptation Costs of a Rolling Stock Schedule with Adaptive Solution: the Case of Demand Changes

In railway scheduling, a nominal traffic schedule is established well in advance for the main resources: train-paths, rolling stock and crew. However, it has to be adapted each time a change in the input data occurs. In this paper, we focus on the costs in the adaptation phase. We introduce the concept of adaptive nominal solution which minimizes adaptation costs with respect to a given set of potential changes. We illustrate this framework with the rolling stock scheduling problem with scenarios corresponding to increasing demand in terms of rolling stock units. We define adaptation costs for a rolling stock schedule and propose two MILPs. The first one adapts, at minimal cost, an existing rolling stock schedule with respect to a given scenario. The second MILP considers a set of given scenarios and computes an adaptive nominal rolling stock schedule together with an adapted solution to each scenario, again while minimizing adaptation costs. We illustrate our models with computational experiments on realistic SNCF instances.