A stochastic dynamic programming approach for delay management of a single train line

Railway delay management considers the question of whether a train should wait for a delayed feeder train. Several works in the literature analyze these so-called wait-depart decisions. The underlying models range from rules of thumb to complete network optimizations. Almost none of them account for uncertainties regarding future delays. In this paper, we present a multi-stage stochastic dynamic programming (SDP) model to make wait-depart decisions in the presence of uncertain future delays. The SDP approach explicitly accounts for potential recourse actions at later stations in a look-ahead manner when making the decision in the current stage. The objective is to minimize the total delay experienced by passengers at their final station by recursively solving Bellman equations. We focus on a single train line but consider the effects on direct feeder and connecting trains. In an extensive numerical study, we compare the solution quality and computational effort of the SDP to other optimization approaches and simple heuristic decision rules that are frequently used in delay management. The SDP approach outperforms the other approaches in almost every scenario with regard to solution quality in reasonable time and seems to be a promising starting point for stochastic dynamic delay management with interesting future research opportunities.