To solve the L.P.P. by Big M. method, various steps are given below:
(i) Express the problem in standard form by introducing slack variables, surplus variables and artificial variables as required in the problem.
(ii) Add non-negative artificial variables to the left side of each of the equations corresponding to constraint of the type =, and ≥. These variables do not appear in the final solution. This is achieved by assigning very large penalty (–M for maximization) in the objective function.
(iii) Solve the modified L.P.P. by simplex method until any one of three cases may arise:
1. If no artificial variables appears in the basis and optimality conditions of simplex method is satisfied, then initial solution is an optimum basic feasible solution.
2. If at least one artificial variable appears in the optimum basis at zero level and the optimality conditions of simplex method are satisfied, then the current solution is an optimum basic feasible solution.
3. If at least one artificial variable appears in the basis at positive level and optimality condition of simplex method is satisfied, then the problem has no feasible solution.
