The Big-M method is an alternative method of solving a linear programming problem involving artificial variables. In this method we assign a very high penalty(say M) to the artificial variables in the objective function. The iterative procedure of the algorithm is given below:

Step 1. Write the given L.P.P. into its standard form and check whether there exists a starting basic feasible solution.
(a) If there is a ready starting basic feasible solution, move on to Step 3.

(b) If there does not exist a ready starting basic feasible solution, move on to Step 2.

Step 2. Add artificial variables to the left side of each equation that has no obvious starting basic variables. Assign a very high penalty (say M) to these variables in the objective function.

Step 3. Apply simplex method to the modified L.P.P. Following cases may arise at the last iteration:

(a) At least one artificial variable is present in the basis with zero value. In such a case the current optimum basic feasible solution is degenerate.

(b) At least one artificial variable is present in the basis with a positive value. In such a case, the given L.P.P. does not possess an optimum basic feasible solution. The given problem is said to have a pseudo-optimum basic feasible solution.
By-Radharani Panigrahi