An eigenmodel for iterative line planning, timetabling and vehicle scheduling in public transportation

•We present a generic, bi-objective model for integrating line planning, timetabling, and vehicle scheduling.•We propose an Eigenmodel for the design of re-optimization procedures in public transportation.•We illustrate the usage of the Eigenmodel on three examples.•We present theoretical results on the convergence of iterative algorithms.•We present a matching approach for re-optimizing the line plan if a timetable is given.

Planning a public transportation system is a multi-objective problem which includes among others line planning, timetabling, and vehicle scheduling. For each of these planning stages, models are known and advanced solution techniques exist. Some of the models focus on costs, others on passengers' convenience. Setting up a transportation system is usually done by optimizing each of these stages sequentially.In this paper we argue that instead of optimizing each single step further and further it would be more beneficial to consider the whole process in an integrated way. To this end, we develop and discuss a generic, bi-objective model for integrating line planning, timetabling, and vehicle scheduling. We furthermore propose an eigenmodel which we apply for these three planning stages and show how it can be used for the design of iterative algorithms as heuristics for the integrated problem. The convergence of the resulting iterative approaches is analyzed from a theoretical point of view. Moreover, we propose an agenda for further research in this field.