Revenue Maximizing Tariff Zone Design For Public Transport Companies
Sven Müller, Universität Hamburg, Knut Haase, Universität Hamburg
A new model to the tariff-zone design problem is presented. The distinct feature of our model is (in contrast to other approaches), that we consider demand to be endogenous and customers choose the time-shortest-path.
Although tariff-zones are applied by the majority of public transport service providers, literature is lacking of quantitative planning approaches which involve the design of tariff-zones and the determination of the corresponding fare (price per zone). We propose a combined fare and tariff-zone planning problem. A set of transport analysis zones (TAZ) for which a given fare has to be paid is considered as a tariff-zone. The tariff the customer has to pay for her trip between two TAZ is the product of the number of tariff-zones passed on this trip and the fare. The objective is to maximize the expected overall revenue (demand times tariff) taking into account contiguous tariff-zones and discrete fare-levels. Contiguity is a complex task in spatial optimization. Here, contiguity is achieved using primal and dual graph information. The primal graph consists of the borders of the TAZ and the dual graph is the public transport network.
The approach proposed is general in the vein that the expected revenue can be determined by any arbitrarily chosen demand model. Demand is measured as the number of public transport trips between TAZ. Here we employ a mixed multinomial logit model because of its generality (i.e. the property to approximate any random utility model).
We perform s series of numerical investigations using GAMS/CPLEX and artificial data to show the applicability of our approach. Further, we employ our approach to the San Francisco Bay Area, California. Based real demand data we investigate the influence of the value-of-travel-time on the spatial pattern of the tariff-zones.
Association for European Transport