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 re-routing 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.

[1]  K. Nachtigall.  Periodic network optimizationi and fixed interval timetables , 1999 .

[2]  Leon Peeters,et al.  The Computational Complexity of Delay Management , 2005, WG.

[3]  Leena Suhl,et al.  Requirement for, and Design of, an Operations Control System for Railways , 1999 .

[4]  Anita Schöbel,et al.  To Wait or Not to Wait? The Bicriteria Delay Management Problem in Public Transportation , 2007, Transp. Sci..

[5]  Martine Labbé,et al.  Optimization models for the single delay management problem in public transportation , 2008, Eur. J. Oper. Res..

[6]  Peter Widmayer,et al.  Railway Delay Management: Exploring Its Algorithmic Complexity , 2004, SWAT.

[7]  Dennis Huisman,et al.  The New Dutch Timetable: The OR Revolution , 2008, Interfaces.

[8]  Michael Gatto,et al.  On the Impact of Uncertainty on some Optimization Problems: Combinatorial Aspects of Delay Management and Robust Online Scheduling , 2007 .

[9]  B. Schutter,et al.  On max-algebraic models for transportation networks , 1998 .

[10]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[11]  Peter Widmayer,et al.  Online Delay Management on a Single Train Line , 2004, ATMOS.

[12]  Michael Schachtebeck,et al.  Delay Management in Public Transportation: Capacities, Robustness, and Integration , 2010 .

[13]  Anita Schöbel,et al.  IP-based Techniques for Delay Management with Priority Decisions , 2008, ATMOS.

[14]  Christian Liebchen,et al.  The First Optimized Railway Timetable in Practice , 2008, Transp. Sci..

[15]  Vinod Chachra,et al.  Applications of graph theory algorithms , 1979 .

[16]  Rob M.P. Goverde,et al.  The Max-plus Algebra Approach To RailwayTimetable Design , 1998 .

[17]  Leena Suhl,et al.  Managing and Preventing Delays in Railway Traffic by Simulation and Optimization , 2001 .

[18]  Anita Schöbel,et al.  DisKon - Disposition und Konfliktlösungsmanagement für die beste Bahn , 2005 .

[19]  Anita Schöbel,et al.  A Model for the Delay Management Problem based on Mixed-Integer-Programming , 2001, ATMOS.

[20]  Anita Schöbel,et al.  Capacity constraints in delay management , 2009, Public Transp..

[21]  Anita Schöbel,et al.  Integer Programming Approaches for Solving the Delay Management Problem , 2004, ATMOS.

[22]  Anita Schöbel,et al.  To Wait or Not to Wait - And Who Goes First? Delay Management with Priority Decisions , 2010, Transp. Sci..

[23]  KroonLeo,et al.  The New Dutch Timetable , 2009 .