Computational Procedures for Solving Linear Programming Problems
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.
KeywordsBasic Solution Linear Programming Problem Basic Variable Transportation Problem Slack Variable
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- 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.See A. Charnes and W.W. Cooper (1954).Google Scholar
- 1.Cf. S. Vajda (1958), p. 4. For further computational short cuts see op. cit., Chs. II and X.Google Scholar
- 3.Cf. A. Charnes and W. W. Cooper, op. cit., pp. 60 ff.Google Scholar