Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art Operations Research models and techniques used in passenger railway transportation. For each planning phase (strategic, tactical and operational), we describe the planning problems arising there and discuss some models and algorithms to solve them. We do not only consider classical, well-known topics such as timetabling, rolling stock scheduling and crew scheduling, but we also discuss some recently developed topics as shunting and reliability of timetables. Finally, we focus on several practical aspects for each of these problems at the largest Dutch railway operator, NS Reizigers.