Delay Management in Public Transportation: Capacities, Robustness, and Integration

Abstract

In this work, we mainly deal with capacitated delay management that is an important task during the daily operations of a public transportation company. Unlike uncapacitated delay management studied in most publications, it takes into account the limited capacity of the track system in a railway setting and security distances between two trains using the same infrastructure.We introduce a graph-theoretical model for this problem and derive a linear integer program, based on the graph-theoretical model. We prove some important properties of the model which allow us to extend results from the uncapacitated delay management problem to the capacitated case. Furthermore, we use these properties to develop reduction techniques which can significantly reduce the size of an input instance. To be able to solve large-scale real-world instances, we suggest heuristic solution procedures, prove worst-case error bounds, and numerically evaluate all solution approaches within a case study based on real-world data. We show how rolling stock circulations can be integrated in the delay management problem, extend results from capacitated delay management to this integrated problem, prove that it is NP-hard even in very special cases, identify a polynomially solvable case, and suggest a generic solution framework.Apart from delay management, we also consider robustness aspects. We report results from a case study on delay resistant timetabling, resume the concept of recoverable robustness, extend it to multi-stage recoverable robustness, and show how both concepts can be applied to special timetabling problems to compute recoverable-robust timetables. In the end, we present a programming framework for analyzing the impact of different planning stages in public transportation on subsequent planning stages and on the operational phase, for example for analyzing the robustness of a line plan or a timetable in case of delays.