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Networks and Basic Solutions

Author

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  • Ellis L. Johnson

    (Yale University, New Haven, Connecticut)

Abstract

A labeling procedure which could be used to carry out the steps of the simplex algorithm for a network flow problem is given. A modification of the simplex algorithm for the maximum flow problem is suggested which is equivalent to the Ford-Fulkerson algorithm if the solutions are kept basic in the latter. A procedure to keep the solutions basic in the Ford-Fulkerson algorithm is given. An example of a flow with gains problem with integer capacities and gains is given for which the usual labeling procedure may not lead to an optimum solution if the solutions are not kept basic. Extension of the network flow techniques to flows with gains is discussed.

Suggested Citation

  • Ellis L. Johnson, 1966. "Networks and Basic Solutions," Operations Research, INFORMS, vol. 14(4), pages 619-623, August.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:4:p:619-623
    DOI: 10.1287/opre.14.4.619
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    Cited by:

    1. Martin, Peter T., 1995. "Turning Movement Estimation In Real Time (TMERT)," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3rp1v8fs, Institute of Transportation Studies, UC Berkeley.
    2. M. A. Venkataramana & John J. Dinkel & John Mote, 1991. "Vector processing approach to constrained network problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 71-85, February.
    3. Prahalad Venkateshan & Kamlesh Mathur & Ronald H. Ballou, 2008. "An efficient generalized network-simplex-based algorithm for manufacturing network flows," Journal of Combinatorial Optimization, Springer, vol. 15(4), pages 315-341, May.
    4. P. Beraldi & F. Guerriero & R. Musmanno, 1997. "Efficient Parallel Algorithms for the Minimum Cost Flow Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 501-530, December.
    5. Sulin Ba & Jan Stallaert & Andrew B. Whinston, 2001. "Optimal Investment in Knowledge Within a Firm Using a Market Mechanism," Management Science, INFORMS, vol. 47(9), pages 1203-1219, September.

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