Railway delay management with passenger rerouting considering train capacity constraints

Delay management for railways is concerned with the question of whether a train should wait for a delayed feeder train or depart on time. The answer should not only depend on the length of the delay but also consider other factors, such as capacity restrictions. We present an optimization model for delay management in railway networks that accounts for capacity constraints on the number of passengers that a train can effectively carry. While limited capacities of tracks and stations have been considered in delay management models, passenger train capacity has been neglected in the literature so far, implicitly assuming an infinite train capacity. However, even in open systems where no seat reservation is required and passengers may stand during the journey if all seats are occupied, physical space is naturally limited, and the number of standing seats is constrained for passenger safety reasons. We present a mixed-integer nonlinear programming formulation for the delay management problem with passenger rerouting and capacities of trains. Our model allows the rerouting of passengers missing their connection due to delays or capacity constraints. We linearize the model in exact and approximate ways and experimentally compare the different approaches with the solution of a reference model from the literature that neglects capacity constraints. The results demonstrate that there is a significant impact of considering train capacity restrictions in decisions to manage delays.