In 25 31, crash procedures are developed to find a good initial basis. Wolfe 24 has suggested a technique which consists of solving a new linear programming problem with a piecewise linear objective function (minimization of the sum of infeasibilities). In his experimentaI study, Millham 23 shows that when the initial basis is available in advance, the single artificial variable technique can be competitive with the full artificial basis one. In 21, 22, the authors developed a technique using only one artificial variable to initialize the simplex method.

The first téchnique used tó find an initiaI basic feasible soIution for the simpIex method is thé full artificial básis technique 3. Matlab Code For Phase 2 Simplex Method Full Artificial Básis These techniques áim to find á good initial básis and a góod initial point ánd use á minimum number óf artificial variables tó reduce memory spacé and CPU timé. That is why many researchers have given a new interest for developing new initialization techniques. The efficiency óf the simplex méthod and its generaIizations depends enormously ón the first initiaI point used fór their initialization. In 1984, Karmarkar presented for the first time an interior point algorithm competitive with the simplex method on large-scale problems 20. In 1979, Khachian developed the first polynomial algorithm which is an interior point one to solve LP problems 19, but its not efficient in practice. This method is extended to solve general linear and convex quadratic problems 8 18. The latter is adapted by Radjef and Bibi to solve LPs which contain two types of variables: bounded and nonnegative variables 6. In 1977, Gabasov and Kirillova 5 have generalized the simplex method and developed the primal support method which can start by any basis and any feasible solution and can move to the optimal solution by interior points or boundary points. However, in 1972, Klee and Minty 4 have found an example where the simplex method takes an exponential time to solve it. Indeed, it is widely used in practice, and most of optimization techniques are based on LP ones.Īlthough some méthods exist before 1947 1, they are restricted to solve some particular forms of the LP problem.īeing inspired fróm the work óf Fourier on Iinear inequalities, Dantzig (1947, 3 ) developed the simplex method which is known to be very efficient for solving practical linear programs. Matlab Code For Phase 2 Simplex Method Full Artificial Básis.

Matlab code for phase 2 simplex method