Skip to main content
SpringerLink
Log in

On the equivalence of some generalized network problems to pure network problems

  • Published:
Mathematical Programming Submit manuscript

Abstract

The purpose of this paper is to show that any generalized network problem whose matrix does not have full row rank can be transformed into an equivalent pure network problem and to give a constructive method for doing this.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Balas, “The dual method for the generalized transportation problem”,Management Science 12 (7) (1966) 555–568.

    Google Scholar 

  2. E. Balas and P.L. Ivanescu (Hammer), “On the generalized transportation problem”,Management Science 11 (1) (1964) 188–202.

    Google Scholar 

  3. A. Charnes and W.W. Cooper,Management models and industrial applications of linear programming, Volumes 1 and 2 (Wiley, New York, 1961).

    Google Scholar 

  4. A. Charnes and W.M. Raike, “One-pass algorithms for some generalized network problems”,Operations Research 14 (5) (1966) 914–924.

    Google Scholar 

  5. G. Dantzig,Linear programming and extensions (Princeton Univ. Press, Princeton, N.J., 1963).

    Google Scholar 

  6. K. Eisemann, “The generalized stepping-stone method for the machine loading model”,Management Science 11 (1) (1964) 154–177.

    Google Scholar 

  7. F. Glover and D. Klingman, “Locating stepping-stone paths in distribution problems via the predecessor index method”,Transportation Science 4 (2) (1970) 220–225.

    Google Scholar 

  8. F. Glover, D. Karney and D. Klingman, “The augmented predecessor index method for locating stepping-stone paths and assigning dual prices in distribution problems”,Transportation Science 6 (2) (1972) 171–180.

    Google Scholar 

  9. F. Glover, D. Karney, D. Klingman and A. Napier, “A comparison of computation times for various starting procedures, basis change criteria and solution algorithms for transportation problems”,Management Science, to appear.

  10. F. Glover, D. Klingman and A. Napier, “Basic dual feasible solutions for a class of generalized networks”,Operations Research 20 (1972) 126–137.

    Google Scholar 

  11. W.S. Jewell, “Optimal flow through networks with gains”,Operations Research 10 (4) (1962) 476–499.

    Google Scholar 

  12. J. Lourie, “Topology and computation of the generalized transportation problem”,Management Science 11 (1) (1964) 177–187.

    Google Scholar 

  13. W.R. Lynn and A. Charnes, “The dyadic computation of a generalized network model of a sewage treatment system”, ONR Research Memorandum No. 19, Northwestern University, Evanston, Ill. (1959).

    Google Scholar 

  14. M. Simmonnard,Linear programming, translated by W.S. Jewell (Prentice-Hall, Englewood Cliffs, N.J., 1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Colorado, Boulder, Colo., USA

    Fred Glover & D. Klingman

  2. The University of Texas, Austin, Texas, USA

    Fred Glover & D. Klingman

Authors
  1. Fred Glover
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Klingman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glover, F., Klingman, D. On the equivalence of some generalized network problems to pure network problems. Mathematical Programming 4, 269–278 (1973). https://doi.org/10.1007/BF01584670

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01584670

Keywords

Search

Navigation