A Team-Orienteering Model for Optimising Fare Inspector Itineraries in Public Transport Networks

Fare evasion, defined as the act of using public transport without paying the required fare, poses a significant challenge to the financial viability of public transport systems. Fare inspection is accordingly employed as a key control mechanism to verify that passengers have paid the appropriate fare for their journey, thereby protecting the revenue of public transport operators. Regular and visible ticket inspections increase the perceived risk of detection, thus discourage fare evasion and promote a culture of fare compliance. Many studies have shown that fare evasion rates are responsive to changes in fare inspection strategies, highlighting the importance of establishing effective inspection methods. Traditional approaches of formalising fare inspection strategies rely on individual behaviour assumptions and data collected from onboard surveys. The emergence of automatically collected data, such as Automatic Passenger Counting (APC) and Automatic Fare Collection (AFC) systems, offers new opportunities for more precise fare evasion measurement. This data can serve as a robust reference for developing fare inspection strategies with real-time inputs, both in terms of planning and execution. This research proposes a dynamic modelling framework that integrates automatically collected data to optimise ticket inspection strategies. The model is formulated as a team-orienteering problem and solved using mixed-integer programming, accounting for, on one hand, the deterrent effect of fare evaders by inspections, and on the other hand, the decay of this deterrent effect over time. A case study on the Melbourne tram network demonstrates the model's potential to generate optimised ticket inspection itineraries under different assumptions of passengers behaviour. This model will assist public transport operators in dynamically adjusting ticket inspection strategies based on real-time automated data. Finally, the policy implications of the proposed model for optimal operations of fare inspections are discussed and potential advantages and drawbacks are highlighted.