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Design of Zone Tariff Systems in Public Transportation

Department of Mathematics, Universität Kaiserslautern, 67663 Kaiserslautern, Germany
Department of Numerical and Applied Mathematics, University of Göttingen, 37083 Göttingen, Germany
hamacher{at}mathematik.uni-kl.de
schoebel{at}math.uni-goettingen.de

Dedicated to our doctor father and grandfather, Prof. Dr. E. Rainer Burkard, on the occasion of his 60th birthday

Given a public transportation system represented by its stops and direct connections between stops, we present OR models for two problems dealing with the prices for the customers. In the first, the fare problem, 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. The second problem, the zone problem includes the design of the zones. In an exemplary way we study this problem for one of the objectives. It 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.

Subject classifications: integer programming; algorithms, heuristics, applications; transportation; models, traffic.
History: Received May 2001; revision received August 2002; revision received January 2003; revision received July 2003; accepted July 2003.