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To Wait or Not to Wait? The Bicriteria Delay Management Problem in Public Transportation

Institut für Numerische und Angewandte Mathematik, Georg-August Universität, Göttingen, Lotzestr 16-18, D-37083, Göttingen, Germany
Institut für Numerische und Angewandte Mathematik, Georg-August Universität, Göttingen, Lotzestr 16-18, D-37083, Göttingen, Germany
ginkel{at}math.uni-goettingen.de
schoebel{at}math.uni-goettingen.de

Assume that a train reaches a station with delay. At the station there is a bus ready to depart. The question of whether the bus should wait for the delayed train or depart on time is called the delay management problem. Different single objective functions for this problem have been introduced and analyzed. In this paper, we present a bicriteria model for the delay management problem, taking into account both the delay of the vehicles and the number of passengers who miss a connection. Our model does not depend on detailed data about the passengers and hence can be easily implemented in practice.

To analyze the problem, we present an integer programming formulation and a graph-theoretic approach that is based on discrete time/cost trade-off project networks. Using results of project planning, we develop an efficient solution method. We tested our procedure using real-world data. The results show the applicability of the approach.

Key Words: public transit operations; delay management; discrete time-cost trade-off problem
History: Received: January 2003; revised: May 2007; accepted: July 2007.