The simplex method is a technique of tackling linear programming problems and it requires that the problems are presented in their standard form. However, not all linear programming tasks are expressed in standard form.
In most cases, the constraints are presented as inequalities and not equations. In other cases, the decision variables are not even nonnegative. Therefore the central procedure of solving linear programming tasks is converting the problem to its standard form. Some of the ways a linear problem can be converted into a standard form are by converting the inequalities into equalities, converting the decision variables to have nonnegative signs and making the constraints’ right-hand sides to be nonnegative. According to Tempelmeier et al. (258), linear programming tasks that entail two variables can be solved using the graphical solution technique. However, for those involving more than three variables, the simplex method is the most convenient. The simplex method was established in 1946 by George Dantzig and it provides a systematic technique of solving linear programming techniques. The technique creates an organized formula of examining the vertices’ feasible areas, which aid in the calculations of the optimal value of an objective function.
The simplex method is used to curb the challenges in linear programming. Generally, the technique is exceptionally powerful as it can be used to detect whether a solution exists or not (Tempelmeier 259). The simplex technique employs a unique strategy for generating and testing potential vertex solutions in linear programming. For every iteration, the simplex methods identify the most suitable variables that result in the greatest modifications towards the minimum solution.
Generally, the simplex method substantially aids in the eradication of problems in linear programming that involves more than two variables. The method is powerful and is used to examine whether a solution to a linear program problem exists or not.
Tempelmeier, Horst, Michael Kirste, and Timo Hilger. “Linear programming models for a
stochastic dynamic capacitated lot sizing problem.” Computers & Operations Research 91