In proof-of-payment systems, fare evasion represents a crucial topic for public transport companies (PTCs) due to lost fare revenues, damaged corporate image, and increased levels of violence on public transport, which might also have negative economic repercussions on PTCs. Therefore, there is a need to establish the level of inspection (i.e. the number of inspectors) to tackle fare dodgers as a possible option. By building on previous models, this paper develops a formal economic framework to derive the optimum inspection level in a long time window, based on system-wide profit maximization when fare evasion exists. The framework takes into account: (i) the refined segmentation of passengers and potential fare evaders, (ii) the variability of perceived inspection level by passengers, and (iii) the fact that an inspector cannot fine every passenger caught evading. Its implementation is illustrated by using three years of real data from an Italian PTC. Based on 27,514 stop-level inspections and 10,586 on-board personal interviews, the results show that the optimum inspection level is 3.8%. Put differently, it is sufficient to check 38 passengers out of every 1000 to maximize profit in the presence of fare evasion. This outcome is very useful, because it improves the one obtained in previous formulations. Indeed, profit maximization is achieved with a lower number of inspectors, thus reducing inspection costs, which are relevant determinants in proficient PTCs. Finally, the framework is flexible and may be applied to public transport modes other than buses as long as proof-of-payment systems are in use.
