Abstract
A new model to the tariff-zone design problem in public transportation is presented. The distinct feature of our model (in contrast to other approaches) is that we consider demand to be endogenous and customers are assumed to 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 contribute to the literature by a new model for the tariff zone design problem. The objective is to maximize the expected total revenue (demand x tariff) taking into account contiguous tariff zones and discrete fare levels. Demand – as a function of tariff (i.e., demand depends on the tariff to be paid) - is measured as the number of public transport trips between origin and destination. Customers are assumed to choose the time-shortest-path (which is confirmed by empirical studies). For a given fare we compute the expected revenue for each origin-destination pair and the number of tariff zones passed. As a consequence we are able to model the original non-linear problem as a MIP. The problem has to be solved for each fare level separately. Contiguity is a complex task in spatial optimization. Here, contiguity is achieved by using primal and dual graph information. Therefore, we consider flow conservation constraints using the dual graph of the public transport graph. Our approach is general in the vein that demand can be determined by any arbitrarily chosen demand model (i.e., no assumptions about the functional form have to be made). We perform a 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 on real data we investigate the trade-off between expected revenue and expected market share of public transport.
Keywords: public transportation, districting, contiguity, revenue management, customer demand
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| alpha: deviation from optimal revenue; ÖPNV: market share of public transportation |