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Basic Dual Feasible Solutions for a Class of Generalized Networks

Author

Listed:
  • Fred Glover

    (University of Colorado, Boulder, Colorado)

  • D. Klingman

    (The University of Texas, Austin, Texas)

  • A. Napier

    (Continental Oil Company, Ponca City, Oklahoma)

Abstract

The generalized network problem and the closely related restricted dyadic problem occur frequently in applications of linear programming. Although they are next in order of computational complexity after pure network or distribution problems, the jump in degree of difficulty is such that, in the most general problem, there exist no algorithms comparable in speed to those for pure networks. In this paper we characterize the properties of a special class of generalized network problems that permit a dual feasible basic solution to be determined in one “pass” through the network. In particular, this class includes the class of pure network problems for which no such procedure has previously existed. Our algorithm also makes it possible to apply Lemke's dual method and the poly-ω technique of Charnes and Cooper in an efficient manner to solve capacitated (pure) network problems.

Suggested Citation

  • Fred Glover & D. Klingman & A. Napier, 1972. "Basic Dual Feasible Solutions for a Class of Generalized Networks," Operations Research, INFORMS, vol. 20(1), pages 126-136, February.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:1:p:126-136
    DOI: 10.1287/opre.20.1.126
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    Cited by:

    1. Marcin Anholcer, 2012. "Algorithm for the stochastic generalized transportation problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(4), pages 9-20.
    2. Marcin Anholcer, 2013. "Stochastic Generalized Transportation Problem with discrete distribution of demand," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 23(4), pages 9-19.
    3. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.

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