Network design, line planning and timetabling in public transport systems with uncertain parameters: A literature review

Understanding and addressing uncertainty is crucial for effective public transport design. This literature review examines key aspects of modelling and optimisation on network design, line planning and timetabling under uncertain conditions. We restrict the analysis to the case where some parameters in those mathematical problems have an uncertain value, that is, either characterised as a probability distribution, scenarios, or updated over multiple stages. The literature reveals the use of a wide range of concepts and models, the most common ones being robustness, multi-period planning, and stochastic programming. The research varies significantly in the selection of parameters to be unknown and/or uncertain and, in turn, those that are predetermined and deterministic. A critical analysis leads us to the following insights. The value of including uncertainty in the optimisation is often not quantified, and real-life applications that can estimate its benefits are scarce. The analysis reveals variations in terminology across different papers, with multiple overlapping and/or different concepts benefiting from similar mathematical approaches, highlighting the complexities researchers face. Our analysis indicates that only few articles use data to derive realistic or accurate scenarios and distributions to be used in stochastic optimisation approaches. Despite these complexities, ongoing advancements in modelling and optimisation techniques offer a promising path towards more effective and resilient public transport systems. These improvements ultimately enhance service quality and increase passenger satisfaction.