Advertisement

Computational Procedures for Solving Linear Programming Problems

  • Sven Danø

Abstract

As we have seen in Ch. II2, the simplex procedure can be described as a systematic method of examining the set of basic feasible solutions, starting in an arbitrary initial basis of m variables (activities) where m is the number of linear restrictions. If the initial basic solution does not satisfy the simplex criterion, we move to a neighboring basis by replacing one of the basic variables, and so forth, until a basic feasible solution is attained in which all of the simplex coefficients are non-positive (in a minimization problem, non-negative). By the Fundamental Theorem, such a solution will be an optimal solution.

Keywords

Basic Solution Linear Programming Problem Basic Variable Transportation Problem Slack Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 4.
    One of the very few examples that exist is constructed by Beale, cf. E. M. L. Beale (1955) or E. O. Heady and W. Candler (1958), pp. 146 ff. Another example is found in N. Nielsen (1956).Google Scholar
  2. 2.
    See A. Charnes and W.W. Cooper (1954).Google Scholar
  3. 1.
    Cf. S. Vajda (1958), p. 4. For further computational short cuts see op. cit., Chs. II and X.Google Scholar
  4. 3.
    Cf. A. Charnes and W. W. Cooper, op. cit., pp. 60 ff.Google Scholar

Copyright information

© Springer-Verlag Wien 1963

Authors and Affiliations

  • Sven Danø
    • 1
  1. 1.University of CopenhagenDänemark

Personalised recommendations