## Design of Zone Tariff Systems in Public Transportation

• Given a public transportation system represented by its stops and direct connections between stops, we consider two problems dealing with the prices for the customers: The fare problem in which subsets of stops are already aggregated to zones and "good" tariffs have to be found in the existing zone system. Closed form solutions for the fare problem are presented for three objective functions. In the zone problem the design of the zones is part of the problem. This problem is NP hard and we therefore propose three heuristics which prove to be very successful in the redesign of one of Germany's transportation systems

Author: H.W. Hamacher, A. Schöbel urn:nbn:de:hbz:386-kluedo-12843 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (21) Report English 2000 2000 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik branch and cut; facets; facility location; hub location; integer programming; valid inequalities Fraunhofer (ITWM) 510 Mathematik

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