Robust design of tariff zones in integrated transport systems

Designing of tariff system in integrated transport system (ITS) is an important issue. There are several approaches how to design a tariff system, for example a division the region into smaller areas - tariff zones can be used. One of the fundamental input data in the zone tariff planning is origin-destination (OD) matrix as the demand matrix which can have a major influence on the system design, but it can usually contain some uncertainties. To deal with this problem and to test robustness of the design several approaches can be used. In this paper we present two integer programming based approaches, one of them is based on the theory of fuzzy sets and second one on the model reformulation with parameters modeling the impact of fare changes on the demand for traveling. We formulate mathematical model of the tariff zones design problem and present both approaches. Designed approaches are verified on the real data set from the Zilina municipality, where we have an OD matrix calculated using passengers' smart card transactions for a period of one week (approx. 110 000 transaction records). To solve the problem we use a universal optimization tool Xpress.