Tuesday, April 21, 2015

Steps of Big-M method of LPP

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Step-1: At first we have to express the a Linear Programming Problem (LPP) to its standard form.
Step-2: Add arificial variable Ri to the left hand side of all constraints of the form = or ≥ types of original LP. 
Step-3: We continue with the regular steps of simplex method.
Step-4: While making iterations using simplex method, one of the following cases may arise-
Case-i: If no artificial variable remains in the positive levels and the optimality condition is satisfied, then the solution is optimal. 
Case-ii: When big M simplex method terminates with an optimum table, it is sometimes possible for one or more artificial variables to remain in the basis as basic variables. It implies that the original problem is infeasible. 
What is artificial variable?
A non negative variable which is added to the left hand side of all constraints of = or ≥ type is called artificial variable. 
This artificial variable is added to obtain an initial basic feasible solution. 
(to be continued) 

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