21-12-2012, 06:50 PM
Artificial Variable Technique (The Big-M Method)
1Artificial Variable.ppt (Size: 175.5 KB / Downloads: 333)
Big-M Method of solving LPP
The Big-M method of handling instances with artificial
variables is the “commonsense approach”. Essentially, the
notion is to make the artificial variables, through their
coefficients in the objective function, so costly or unprofitable
that any feasible solution to the real problem would be
preferred..unless the original instance possessed no feasible
solutions at all. But this means that we need to assign, in the
objective function, coefficients to the artificial variables that are
either very small (maximization problem) or very large
(minimization problem); whatever this value,let us call it Big M.
In fact, this notion is an old trick in optimization in general; we
simply associate a penalty value with variables that we do not
want to be part of an ultimate solution(unless such an outcome
Is unavoidable).
Convert the LP problem into a system of linear equations.
We do this by rewriting the constraint inequalities as equations by subtracting new “surplus & artificial variables" and assigning them zero & +M coefficientsrespectively in the objective function as shown below.