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Formulating and solving the network design problem by decomposition

Author

Listed:
  • Dantzig, George B.
  • Harvey, Roy P.
  • Lansdowne, Zachary F.
  • Robinson, David W.
  • Maier, Steven F.

Abstract

The optimal transportation network design problem is formulated as a convex nonlinear programming problem and a solution method based on standard traffic assignment algorithms is presented. The technique can deal with network improvements which introduce new links, which increase the capacity of existing links, or which decrease the free-flow (uncongested) travel time on existing links (with or without simultaneously increasing link capacity). Preliminary computational experience with the method demonstrates that it is capable of solving very large problems with reasonable amounts of computer time.

Suggested Citation

  • Dantzig, George B. & Harvey, Roy P. & Lansdowne, Zachary F. & Robinson, David W. & Maier, Steven F., 1979. "Formulating and solving the network design problem by decomposition," Transportation Research Part B: Methodological, Elsevier, vol. 13(1), pages 5-17, March.
    • Handle: RePEc:eee:transb:v:13:y:1979:i:1:p:5-17
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    Cited by:

    1. Moreno-Quintero, Eric, 2006. "Optimal control of road freight flows by route choice inducement: A case from Mexico," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1588-1604, December.
    2. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    3. Elnaz Miandoabchi & Reza Farahani & Wout Dullaert & W. Szeto, 2012. "Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks," Networks and Spatial Economics, Springer, vol. 12(3), pages 441-480, September.
    4. Arash Kaviani & Russell G. Thompson & Abbas Rajabifard & Majid Sarvi, 2020. "A model for multi-class road network recovery scheduling of regional road networks," Transportation, Springer, vol. 47(1), pages 109-143, February.
    5. Dung-Ying Lin & Chi Xie, 2011. "The Pareto-optimal Solution Set of the Equilibrium Network Design Problem with Multiple Commensurate Objectives," Networks and Spatial Economics, Springer, vol. 11(4), pages 727-751, December.
    6. Halbach, Daniel Walter, 1991. "A Beginners Guide To Transportation Modeling With Tranplan - A Supplement To Computer Simulation Of Strategies For Managing The Rural Road Infrastructure," Staff Papers 13539, University of Minnesota, Department of Applied Economics.
    7. Anny B. Wang & W. Y. Szeto, 2020. "Bounding the Inefficiency of the Reliability-Based Continuous Network Design Problem Under Cost Recovery," Networks and Spatial Economics, Springer, vol. 20(2), pages 395-422, June.
    8. Gao, Ziyou & Wu, Jianjun & Sun, Huijun, 2005. "Solution algorithm for the bi-level discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(6), pages 479-495, July.
    9. Poorzahedy, Hossain & Rouhani, Omid M., 2007. "Hybrid meta-heuristic algorithms for solving network design problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 578-596, October.
    10. Dung-Ying Lin & Ampol Karoonsoontawong & S. Waller, 2011. "A Dantzig-Wolfe Decomposition Based Heuristic Scheme for Bi-level Dynamic Network Design Problem," Networks and Spatial Economics, Springer, vol. 11(1), pages 101-126, March.
    11. Gallo, Mariano & D'Acierno, Luca & Montella, Bruno, 2010. "A meta-heuristic approach for solving the Urban Network Design Problem," European Journal of Operational Research, Elsevier, vol. 201(1), pages 144-157, February.
    12. Fruin, Jerry E. & Halbach, Daniel Walter, 1992. "Rural Roads, Investment And Disinvestment In A Minnesota County," Staff Papers 13228, University of Minnesota, Department of Applied Economics.
    13. D E Boyce, 1984. "Urban Transportation Network-Equilibrium and Design Models: Recent Achievements and Future Prospects," Environment and Planning A, , vol. 16(11), pages 1445-1474, November.
    14. T. Kim & Sunduck Suh, 1988. "Toward developing a national transportation planning model: A bilevel programming approach for Korea," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 22(1), pages 65-80, February.
    15. Hamid Farvaresh & Mohammad Sepehri, 2013. "A Branch and Bound Algorithm for Bi-level Discrete Network Design Problem," Networks and Spatial Economics, Springer, vol. 13(1), pages 67-106, March.

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