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" tari s 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 succesful in the redesign of one of Germany's transportations systems. 1 Tari systems in public transportation In this paper we deal with the design of tari systems in public transportation, a complex real-world problem, that was brought to our attention by a regional public transportation company several years ago. While working on the design of a fair tari system we both developed a mathematical theory and a visualization tool to evaluate the e ects of tari changes. In this paper we present our studies and experience over the last years in this area. When using a bus or a train, a passenger usually has to pay for his trip. There are several possiblities for de ning ticket prices in public transportation. In a distance tari system, the price for a trip is dependent on the length of the trip. The longer the trip is, the higher is the fare. This system is mostly considered as fair. To determine the ticket prices one needs the distance between each pair of stations. This makes a distance tari inconvenient for the public transportation company and for the customers.