Design of zone tariff systems in public transportation

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.