50 years of Operations Research in public transport

The planning and operations of public transport has benefited from the development and application of Operations Research (OR) techniques in the past half a century. In this article, we describe OR-related techniques and applications in the public transport domain in the last 50 years (1975-2025) since the origin of the intersection of these two research fields. Following a brief description of the public transport planning process, we outline how different topics, models, and solution approaches have evolved throughout this period. For each topic - varying from network assignment, line planning and crew scheduling to real-time management and demand-responsive transport - we review seminal works, key approaches and developments as well as comment on the applicability thereof and recent trends. In addition, we identify primary cross-cutting themes of research: integrating different planning stages, system resilience, dealing with uncertainties and energy-efficient public transport, as well as pricing and equity considerations. Moreover, reinforcement learning and quantum computing are expected to play an increasingly important role in OR applications in public transport. In the next half a century OR in public transport will undoubtedly continue to evolve in response to the technical developments in the transport sector, the developments in algorithms, software and hardware for computing, and by the challenges society faces.