Integer Programming Approaches for Solving the Delay Management Problem

The delay management problem deals with reactions in case of delays in public transportation. More specifically, the aim is to decide if connecting vehicles should wait for delayed feeder vehicles or if it is better to depart on time. As objective we consider the convenience over all customers, expressed as the average delay of a customer when arriving at his or her destination. We present path-based and activity-based integer programming models for the delay management problem and show the equivalence of these formulations. Based on these, we present a simplification of the (cubic) activity-based model which results in an integer linear program. We identify cases in which this linearization is correct, namely if the so-called never-meet property holds. We analyze this property using real-world railway data. Finally, we show how to find an optimal solution in linear time if the never-meet property holds.