A VARIANT OF SIMPLEX METHOD
NISHIDH VILAS LAD-2013176
NITESH SINGH PATEL-2013178
NITIN KUMAR SHUKLA-2013180
WHAT IS BIG-M METHOD?
The Big M method is a method of solving linear programming problems.
It is a variation of the simplex method designed for solving problems typically
encompassing "greater-than" constraints as well as "less-than" constraints -
where the zero vector is not a feasible solution.
The "Big M" refers to a large number associated with the artificial variables,
represented by the letter M.
If optimal solution has any artificial variable with non-zero value, original
problem is infeasible
Four drawbacks of BIG-M method:
How large should M be?
If M is too large, serious numerical difficulties in a computer
Big-M method is inferior than 2 phase method
Here feasibility is not known until optimality
Steps In The Big-M Method
Add artificial variables in the model to obtain a feasible solution.
Added only to the ‘>’ type or the ‘=‘ constraints
A value M is assigned to each artificial variable
The transformed problem is then solved using simplex eliminating the
Important Points To Remember
Solve the modified LPP by simplex method, until
any one of the three cases may arise.
If no artificial variable appears in the basis and the optimality conditions are
If at least one artificial variable in the basis at zero level and the optimality
condition is satisfied
If at least one artificial variable appears in the basis at positive level and the
optimality condition is satisfied, then the original problem has no feasible
Big M Method: Example 1
Minimize Z = 40x1 + 24x2
Subject to 20x1 + 50x2 >= 4800
80x1 + 50x2 >= 7200
x1 , x2 >= 0
Introducing Surplus Variable and Artificial
Variable to obtain an Initial Solution
Minimize Z = 40x1 + 24x2+ 0s1 + 0s2 + MA1 + MA1
Subject to 20x1 + 50x2 –S1 + A1 = 4800
80x1 + 50x2 –S2 + A2 = 7200
x1 , x2 >= 0
S1 and S2 Surplus Variable
A1 and A2 Artificial Variable