The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables — and Beyond

In the planning process of railway companies, we propose to integrate important decisions of network planning, line planning, and vehicle scheduling into the task of periodic timetabling. From such an integration, we expect to achieve an additional potential for optimization. Models for periodic timetabling are commonly based on the Periodic Event Scheduling Problem (PESP). We show that, for our purpose of this integration, the PESP has to be extended by only two features, namely a linear objective function and a symmetry requirement. These extensions of the PESP do not really impose new types of constraints. Indeed, practitioners have already required them even when only planning timetables autonomously without interaction with other planning steps. Even more important, we only suggest extensions that can be formulated by mixed integer linear programs. Moreover, in a self-contained presentation we summarize the traditional PESP modeling capabilities for railway timetabling. For the first time, also special practical requirements are considered that we prove not being expressible in terms of the PESP.