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Network Design with Fixed and Variable Cost Elements

Author

Listed:
  • John W. Billheimer

    (SYSTAN, Inc., Los Altos, California)

  • Paul Gray

    (University of Southern California, Los Angeles, California)

Abstract

A route selection algorithm is presented far designing transportation networks. The algorithm balances fixed construction costs and variable user costs in a network having a fixed set of nodes and a known demand, for internode service. The problem solved is a special case of the fixed-cost, multicommodity transshipment problem in which each commodity has a single, unique source node. The route selection algorithm alternatively applies link elimination and link insertion criteria that converge to a local optimum. Upper and lower bounds on the fixed and variable portions of the globally optimum solution are determined and the sensitivity of the solution is estimated. Unique rules are formulated for identifying links that must or must not appear in the globally optimum solution. The solution procedure has been coded for a digital computer and demonstrated using a representation of Minneapolis-St. Paul having 68 nodes and 476 potential oneway links.

Suggested Citation

  • John W. Billheimer & Paul Gray, 1973. "Network Design with Fixed and Variable Cost Elements," Transportation Science, INFORMS, vol. 7(1), pages 49-74, February.
    • Handle: RePEc:inm:ortrsc:v:7:y:1973:i:1:p:49-74
    DOI: 10.1287/trsc.7.1.49
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    Cited by:

    1. Cantarella, G.E. & Pavone, G. & Vitetta, A., 2006. "Heuristics for urban road network design: Lane layout and signal settings," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1682-1695, December.
    2. K. Ramacandra Rao & Subhro Mitra & Joseph Szmerekovsky, 2021. "Bus Transit Network Structure Selection With Multiple Objectives," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 12(4), pages 1-13, October.
    3. M-G Yoon & J Current, 2008. "The hub location and network design problem with fixed and variable arc costs: formulation and dual-based solution heuristic," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 80-89, January.
    4. Shao, Shuai & Tan, Zhijia & Wang, Tingsong & Liu, Zhiyuan, 2023. "Configuration design of the emission control areas for coastal ships: A Stackelberg game model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 172(C).
    5. Karimi Dehnavi, Hadi & Rezvan, Mohammad Taghi & Shirmohammadli, Abdolmatin & Vallée, Dirk, 2013. "A solution for urban road selection and construction problem using simulation and goal programming—Case study of the city of Isfahan," Transport Policy, Elsevier, vol. 29(C), pages 46-53.
    6. Jenn-Rong Lin & Linda Nozick & Mark Turnquist, 2006. "Strategic design of distribution systems with economies of scale in transportation," Annals of Operations Research, Springer, vol. 144(1), pages 161-180, April.
    7. 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.
    8. Giulio Cantarella & Antonino Vitetta, 2006. "The multi-criteria road network design problem in an urban area," Transportation, Springer, vol. 33(6), pages 567-588, November.
    9. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.

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