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Big M Method

While dealing with linear programming, there are multiple methods that can be used for getting the correct value. This Big M method is one of those methods that are used for linear programming and has its base in the simplex algorithm format. Also, in this case, there are certain ‘greater than’ constraints associated with this method.

Framed by Charnes, this is known as penalty methodand lacks unit matrix which is in tune with coefficient matrix. In order to express the unit matrix in the correct manner, usage of artificial variable is to be made, and to a great extent, it is this addition that creates the change in feasibility of the system which was already lacking behind in terms of equilibrium.

Also, it can be seen that as per simplex method that is used in case of linear programming in most of the cases, it tries to reduce the content associated with artificial variable. In this way both objective functionsare used in best manner as well as feasibility of the equilibrium is restored.

However, this method being a very large number, a simple computer program cannot be developed from this.

Certain important points to note:

These are some of the important factors that need to be taken into consideration to make efficient usage of this procedure.

  • Given that Big M method is merely a variation of the simplex mode of algorithm, it is taken that both multiple and unbounded solution are quite similar.
  • In case of making the optimal table, if it is taken that artificial variable remains with a value that is positive in nature; it is taken as infeasible
  • If it is taken that artificial variable is detached from the basis, it will have no further relation with iterations due to Big M.

These factors if taken into consideration, getting a value from this method becomes easier.

 

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