On Fair Zone Designs in Public Transportation

In this paper we develop some tools for designing balanced zones in public transportation networks. A zone in such a network is a set of stations which are treated as a unit as far as the fares for the passengers are concerned: The zone tariff is only dependent on the starting and ending zones of their travel. A fair zoning is one where the zone tariff is as close as possible to the distance tariff which relates the fare to the actual distance of a customer trip. In particular, the goal of a fair zone design is that neither the public transportation company nor the customer will have major disadvantages in the transition from distance tariff to zone tariff.We will consider three objective functions which model this goal. If the zones are fixed we will show how to choose the tariffs in order to minimize the respective objective functions. This result will be combined with Greedy heuristics to design simultaneously zones and the corresponding tariffs. The paper is concluded by an application of our methods to the data of a regional public transportation company in Germany and a summary of further research in this area.