Operation Research-Simplex Method Procedure And Solved Problems

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This method consists of two phases and its general principle is the following: in the first phase, we start by searching an initial support with the Gauss-Jordan elimination method, then we proceed to the search of an initial feasible solution by solving an auxiliary problem having one artificial variable and an obvious feasible solution.

This obvious feasible solution can be an interior point of the feasible region.

After finding the initial support, we search a feasible solution by adding only one artificial variable to the original problem, thus we get an auxiliary problem with an evident support feasible solution.

An experimental study has been carried out on some NETLIB test problems.

The results of the numerical comparison revealed that finding the initial support by the Gauss elimination method consumes much time, and transforming the equality constraints to inequality ones increases the dimension of the problem.

Hence, the proposed approaches are competitive with the full artificial basis simplex method for solving small problems, but they are not efficient to solve large problems.

In his experimental 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.

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).

We develop a single artificial variable technique to initialize the primal support method for solving linear programs with bounded variables.

We first recall the full artificial basis technique, then we will present the proposed algorithm.


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