Exact approach to the tariff zones design problem in public transport

An integrated transport system is the way how to provide transport service in the region by integrating all modes of transport. The design of this system is connected with solving of several optimization problems such as coordination of connections in transport modes, optimization of connection supply, minimization of time losses related to the changing of travel connection and the design of the tariff configuration. When designing a tariff system, there are several approaches of designing the tariff. One of them is dividing the region into the tariff zones. The price of traveling in such system is determined by the number of traveled tariff zones by the passenger. In this article we analyze the problem, introduce a mathematical model of the tariff zones design problem based on counting zones and introduce two approaches for determining the quality of solution. We will focus on solving this problem using a universal optimization tool Xpress, on test data set of the selected region. We will compare both approaches in terms of computational time and solution quality.