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Modeling Network Transition Constraints with Hypergraphs

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  • Steven Harrod

    (Department of Management Information Systems, Operations Management, and Decision Sciences, University of Dayton, Dayton, Ohio 45469)

Abstract

Discrete time dynamic graphs are frequently used to model multicommodity flows or activity paths through constrained resources, but simple graphs fail to capture the interaction effects of resource transitions. The resulting schedules are not operationally feasible, and return inflated objective values. A directed hypergraph formulation is derived to address railway network sequencing constraints, and an experimental problem sample solved to estimate the magnitude of objective inflation when interaction effects are ignored. The model is used to demonstrate the value of advance scheduling of train paths on a busy North American railway.

Suggested Citation

  • Steven Harrod, 2011. "Modeling Network Transition Constraints with Hypergraphs," Transportation Science, INFORMS, vol. 45(1), pages 81-97, February.
    • Handle: RePEc:inm:ortrsc:v:45:y:2011:i:1:p:81-97
    DOI: 10.1287/trsc.1100.0337
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    1. Gabrio Caimi & Dan Burkolter & Thomas Herrmann & Fabian Chudak & Marco Laumanns, 2009. "Design of a Railway Scheduling Model for Dense Services," Networks and Spatial Economics, Springer, vol. 9(1), pages 25-46, March.
    2. Nguyen, S. & Pallottino, S., 1988. "Equilibrium traffic assignment for large scale transit networks," European Journal of Operational Research, Elsevier, vol. 37(2), pages 176-186, November.
    3. R. Kipp Martin & Ronald L. Rardin & Brian A. Campbell, 1990. "Polyhedral Characterization of Discrete Dynamic Programming," Operations Research, INFORMS, vol. 38(1), pages 127-138, February.
    4. Carey, Malachy, 1994. "A model and strategy for train pathing with choice of lines, platforms, and routes," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 333-353, October.
    5. U. Brännlund & P. O. Lindberg & A. Nõu & J.-E. Nilsson, 1998. "Railway Timetabling Using Lagrangian Relaxation," Transportation Science, INFORMS, vol. 32(4), pages 358-369, November.
    6. Gorman, Michael F., 2009. "Statistical estimation of railroad congestion delay," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(3), pages 446-456, May.
    7. Jovanovic, Dejan & Harker, Patrick T., 1990. "A Decision Support System for Train Dispatching: An Optimization-Based Methodology," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 31(1).
    8. Andrea D'Ariano & Francesco Corman & Dario Pacciarelli & Marco Pranzo, 2008. "Reordering and Local Rerouting Strategies to Manage Train Traffic in Real Time," Transportation Science, INFORMS, vol. 42(4), pages 405-419, November.
    9. Patrice Marcotte & Sang Nguyen & Alexandre Schoeb, 2004. "A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks," Operations Research, INFORMS, vol. 52(2), pages 191-212, April.
    10. Cacchiani, Valentina & Caprara, Alberto & Toth, Paolo, 2010. "Scheduling extra freight trains on railway networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 215-231, February.
    11. Peter J. Zwaneveld & Leo G. Kroon & H. Edwin Romeijn & Marc Salomon & Stéphane Dauzère-Pérès & Stan P. M. Van Hoesel & Harrie W. Ambergen, 1996. "Routing Trains Through Railway Stations: Model Formulation and Algorithms," Transportation Science, INFORMS, vol. 30(3), pages 181-194, August.
    12. Alberto Caprara & Matteo Fischetti & Paolo Toth, 2002. "Modeling and Solving the Train Timetabling Problem," Operations Research, INFORMS, vol. 50(5), pages 851-861, October.
    13. Martland, Carl D., 2008. "Improving On-Time Performance for Long-Distance Passenger Trains Operating on Freight Routes," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 47(4).
    14. Djellab, Housni & Djellab, Khaled & Gourgand, Michel, 2000. "A new heuristic based on a hypergraph representation for the tool switching problem," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 165-176, March.
    15. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    16. Higgins, A. & Kozan, E. & Ferreira, L., 1996. "Optimal scheduling of trains on a single line track," Transportation Research Part B: Methodological, Elsevier, vol. 30(2), pages 147-161, April.
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