The Computational Complexity of Delay Management

Delay management for public transport consists of deciding whether vehicles should wait for delayed transferring passengers, with the objective of minimizing the overall passenger discomfort. We model the underlying transportation network as a directed acyclic graph, where edges represent trains, and weighted paths represent passenger flows. Given initial delays of some of the passenger paths, our goal is to decide which edges wait for delayed passenger paths, such that the sum of all passenger delays is minimized. This paper classifies the computational complexity of delay management problems with respect to various structural parameters, such as the maximum number of passenger transfers, the graph topology, and the capability of edges to reduce delays. Our focus is to distinguish between polynomially solvable and NP-complete problem variants. To that end, we show that even fairly restricted versions of the delay management problem are hard to solve.