Line planning in public transportation: models and methods

The problem of defining suitable lines in a public transportation system (bus, railway, tram, or underground) is an important real-world problem that has also been well researched in theory. Driven by applications, it often lacks a clear description, but is rather stated in an informal way. This leads to a variety of different published line planning models. In this paper, we introduce some of the basic line planning models, identify their characteristics, and review literature on models, mathematical approaches, and algorithms for line planning. Moreover, we point out related topics as well as current and future directions of research.