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,

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... atical approaches, and algorithms for line planning. Moreover, we point out related topics as well as current and future directions of research. Keywords Line planning · Public transportation · Mathematical programming The line planning problem in public transportation Given the increasing demand for mobility, an efficient organization of public (passenger) transportation becomes more and more important. This is reflected not only in practice but also by an increasing number of research papers dealing with the optimization of public transport. The goal of the optimization process is on the one hand, to offer a high quality of service for the passengers while, on the other hand, the costs for setting up and running the transit system should be small. As noted by many authors (see e.g., Ceder and Wilson 1986; Liebchen and Möhring 2007; Desaulniers and Hickman 2007), the planning process in public transportation consists of several consecutive planning phases. As shown in Fig. 1 , the process starts A. Schöbel (B)