A Bi-Objective Optimization Model for Fare Structure Design in Public Transport

Fare planning in public transport is important from the view of passengers as well as of operators. In this paper, we propose a bi-objective model that maximizes the revenue as well as the number of attracted passengers. The potential demand per origin-destination pair is divided into demand groups that have their own willingness how much to pay for using public transport, i.e., a demand group is only attracted as public transport passengers if the fare does not exceed their willingness to pay. We study the bi-objective problem for flat and distance tariffs and develop specialized algorithms to compute the Pareto front in quasilinear or cubic time, respectively. Through computational experiments on structured data sets we evaluate the running time of the developed algorithms in practice and analyze the number of non-dominated points and their respective efficient solutions.