%0 Journal Article
%T A slight modification of the first phase of the simplex algorithm
%A Divni£¿ Tomica
%A Pavlovi£¿ Ljiljana
%J Yugoslav Journal of Operations Research
%D 2012
%I University of Belgrade
%R 10.2298/yjor1006225006d
%X In this paper we give a modification of the first phase procedure for transforming the linear programming problem, given in the standard form min{cTx Ax=b, x¡Ý0}, to the canonical form, i.e., to the form with one feasible primal basis where standard simplex algorithm can be applied directly. The main idea of the paper is to avoid adding m artificial variables in the first phase. Instead, Step 2 of the proposed algorithm transforms the problem into the form with m 1 basic columns. Step 3 is then iterated until the m th basic column is obtained, or it is concluded that the feasible set of LP problem is empty.
%K linear programming
%K simplex algorithm
%K canonical form
%K two phase simplex algorithm
%K new first phase simplex algorithm
%U http://www.doiserbia.nb.rs/img/doi/0354-0243/2012/0354-02431200006D.pdf