## Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (Extended Abstract)

Please always quote using this URN: urn:nbn:de:0297-zib-11076
• Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.

Author: Luis M. Torres, Ramiro Torres, Ralf Borndörfer, Marc E. Pfetsch ZIB-Report computational complexity; integer programming; line planning; public transport 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C27 Combinatorial optimization 2008/12/18 ZIB-Report (08-53) 1438-0064 Appeared in: ATMOS 2008 - 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems. Matteo Fischetti and Peter Widmayer (eds.)Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany, Dagstuhl, Germany, 2008. http://drops.dagstuhl.de/opus/volltexte/2008/1583

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