Parameterizing an Activity Vector in Linear Programming

Chaiho Kim
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Chaiho Kim: University of Santa Clara, Santa Clara, California

Operations Research, 1971, vol. 19, issue 7, 1632-1646

Abstract: This paper presents an algorithm that will parameterize an activity vector for a linear programming problem in the following manner. Assume that an optimum feasible basis for a parametric linear programming problem has been obtained for the low-bound value of the parameter θ, set to zero. The algorithm then determines a sequence of critical values θ 1 , …, θ k , …, θ T , where θ k ≧ θ k −1 , and a series of bases B 1 , …, B k , …, B T , in such a way that B k is optimum feasible for θ k ≦ θ ≦ θ k +1 for 1 ≦ k ≦ T − 1 and B T is either optimum feasible for all θ T ≦ θ ≦ γ or unbounded or infeasible for 0 ≦ θ − θ T ≦ ϵ, where ϵ is an arbitrarily small positive number. The essence of the algorithm consists of a series of simple transformations from one optimum feasible basis to another. The algorithm is illustrated with a numerical example.

Date: 1971
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