Moving Towards a More Accurate Level of Inspection Against Fare Evasion in Proof-of-Payment Transit Systems Benedetto Barabino 1,2 & Sara Salis 2 # Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract This paper proposes an accurate economic framework to determine the optimum inspection level—the number of ticket inspectors—in a long time window, in order to maximize the system-wide profit when fare evasion occurs. This is the first framework that introduces: i) a refined characterization of the passenger demand, ii) a profit function with new constraints, iii) an alternative estimation of the percentage of passengers who choose to evade, and iv) a new formulation accounting for inspectors who cannot fine every passenger caught evading. The implementation of this framework is illustrated by using six years of data gathered from an Italian public transport company. Based on 57,256 stop-level inspections and 21,827 on- board personal interviews, the optimum inspection rate maximizing the profit is in the range of 3.4%-4.0%. This outcome provides more accurate results, which are discussed and compared to previous research. Finally, the framework is flexible, and it may be applied to any urban context in which proof-of-payment systems are adopted. Keywords Fare evasion . Proof-of-payment . Level of inspection . Profit maximization model . Constrained function . Empirical support 1 Introduction Ticket sales represent a relevant source of revenue for Public Transport Companies (PTCs) and help maintain the service at an economically viable level. For instance, Networks and Spatial Economics https://doi.org/10.1007/s11067-019-09468-3 * Sara Salis sara.salis@ctmcagliari.it Benedetto Barabino bbarabino@gmail.com 1 Department of Civil Engineering, Architecture and Environment, University of Cagliari, via Marengo, 09123 Cagliari, Italy 2 Department of Studies and Researches, CTM SpA, viale Trieste 159/3, 09123 Cagliari, Italy