Delay Management with Re-Routing of Passengers

Trains often arrive delayed at stations where passengers have to change to other trains. The question of delay management is whether these trains should wait for the original train or depart on time. In traditional delay management models passengers always take their originally planned route. This means, they are in case of a missed connection always delayed with the cycle time of the timetable. In this paper, we propose a model where rerouting of passengers is incorporated. To describe the problem we represent it as an event-activity network similar to the one used in traditional delay management, with some additional events to incorporate origin and destination of the passengers. We prove NP-hardness of this problem, and we present an integer programming formulation for which we report the first numerical results. Furthermore, we discuss the variant in which we assume fixed costs for maintaining transfers and we present a polynomial algorithm for the special case of only one origin-destination pair.