Models for railway timetable optimization: Applicability and applications in practice

- Matching between types of railway companies and timetable optimization models.
- Overview of assumptions and properties of well-established timetabling models.
- Overview of assumptions and properties of selected robust timetabling models.
- Collection of projects where timetable optimization is applied in practice.

This paper provides an overview of railway timetable design in practice and the combinatorial optimization models that have been proposed for this application, putting emphasis on passenger railway services in the European railway market.We start with a description of the role of the timetable for a railway system, including the perspective of both types of railway companies: train operating companies (TOC) and infrastructure managing companies. We elaborate on the different subprocesses in timetable design that have to be conducted, some of which are exclusive to TOCs, while others are in the responsibility of the infrastructure manager.The two major streams of combinatorial optimization models for railway timetabling must not be understood as concurring models. Rather, they address different subprocesses, even with a focus on different types of railway companies. In this paper we provide a comparison of the different approaches on a number of relevant criteria.Having sketched the major streams we list methods that have been developed for improving the robustness of timetables, including stochastic optimization models and light robustness models. We also provide a description of a number of applications of timetable planning models in practice. We conclude this paper with some topics for further research.