Fare Structure Design in Public Transport

TL;DR

This paper investigates the problem of designing fare structures in public transport by minimizing deviations from reference prices while satisfying constraints like no-elongation and no-stopover, analyzing different fare strategies and their computational complexity.

Contribution

It formulates the fare structure design problem for various fare strategies, analyzes its complexity, and connects it to median problems, providing insights into solvability and constraints.

Findings

Fare structure design can be modeled as a median problem.

Complexity varies from linear-time solvable to NP-complete.

Constraints like no-elongation influence the problem's complexity.

Abstract

Fare planning is one among several steps in public transport planning. Fares are relevant for the covering of costs of the public transport operator, but also affect the ridership and the passenger satisfaction. A fare structure is the assignment of prices to all paths in a network. In practice, often a given fare structure shall be changed to fulfill new requirements, meaning that a new fare strategy is desired. This motivates the usage of prices of the former fare structure or other desirable prices as reference prices. In this paper, we investigate the fare structure design problem that aims to determine fares such that the sum of absolute deviations between the new fares and the reference prices is minimized. Fare strategies that are considered here are flat tariffs, affine distance tariffs and zone tariffs. Additionally, we regard constraints that ensure that it is not beneficial to buy a ticket for a longer journey than actually traveled (no-elongation property) or to split a ticket into several sub-tickets to cover a journey (no-stopover property). Our literature review provides an overview of the research on fare planning. We analyze the fare structure design problem for flat, distance and zone tariffs, pointing out connections to median problems. Further, we study its complexity which ranges from linear-time solvability to NP-complete cases.