To Wait or Not to Wait—And Who Goes First? Delay Management with Priority Decisions

Delay management is an important issue in the daily operations of any railway company. The task is to update the planned timetable to a disposition timetable in such a way that the inconvenience for the passengers is as small as possible. The two main decisions that have to be made in this respect are the wait-depart decisions, to decide which connections should be maintained in case of delays, and the priority decisions, which determine the order in which trains are allowed to pass a specific piece of track. The latter are necessary to take the limited capacity of the track system into account. While the wait-depart decisions have been intensively studied in the literature, the priority decisions in the capacitated case have been neglected so far in delay management optimization models. In the current paper, we add the priority decisions to the integer programming formulation of the delay management problem and are hence able to deal with the capacitated case. The corresponding constraints are disjunctive constraints leading to cycles in the resulting event-activity network. Nevertheless, we are able to derive reduction techniques for the network that enable us to extend the formulation of the never-meet property from the uncapacitated delay management problem to the capacitated case. We then use our results to derive exact and heuristic solution procedures for solving the delay management problem. The results of the algorithms are evaluated both from a theoretical and a numerical point of view. The latter has been done within a case study using the railway network in the region of Harz, Germany.