Big M Method Linear Programming Pdf
Big m method Linear Programming ExampleSo far, we have seen the linear programming constraints with less than type. We come across problems with ‘greater than’ and ‘equal to’ type also. Each of these types must be converted as equations. In case of ‘greater than’ type, the constraints are rewritten with a negative surplus variable s 1 and by adding an artificial variable a.Artificial variables are simply used for finding the initial basic solutions and are thereafter eliminated. In case of an ‘equal to’ constraint, just add the artificial variable to the constraint.
The co-efficient of artificial variables a 1, a 2. Are represented by a very high value M, and hence the method is known as BIG-M Method. Big m method Minimization ProblemThe Big m method minimization problem are explained belowExample: Solve the following LPP using Big M Method.Minimize Z = 3x 1 + x 2Subject to constraints4x 1 + x 2 = 4.(i)5x 1 + 3x 2≥ 7.(ii)3x 1 + 2x 2≤ 6.(iii)where x 1, x 2≥0Solution: Introduce slack and auxiliary variables to represent in the standard form. Constraint 4x 1 + x 2 = 4 is introduced by adding an artificial variable a 1, i.e., 4x 1 + x 2 + a 1 = 4 Constraint, 5x 1 + 3x 2≥ 7 is converted by subtracting a slack s 1 and adding an auxiliary variable a 2.5x 1+ 3x 2– s 1 + a 2 = 7Constraint 3x 2 + 2x 2≤ 6 is included with a slack variable s 23x 2 + 2x 2 + s 2 = 6The objective must also be altered if auxiliary variables exist. If the objective function is minimization, the co-efficient of auxiliary variable is +M (and -M, in case of maximization)The objective function is minimization,Minimize Z = 3x 1+ x 2 + 0s 1+ 0s 2+ Ma 1+ Ma 2z min = 3x 1 + x 2+ Ma 1+ Ma 2The initial feasible solution is (Put x 1, x 2, s 1 = 0)a 1 = 4a 2 = 7s 2 = 6Establish a table as shown below and solve:Simplex TableThe solution is,x 1 = 5/7 or 0.71x 2 = 8/7 or 1.14z min = 3 x 5 / 7 + 8/7= 23/7 or 3.29.
Use The Big M Method To Solve The Following Lps
Quantitative Techniques – Introduction.Measures Of Central Tendency.Mathematical Model.Linear Programming: Graphical Method.Linear Programming: Simplex Method.Transportation Model.Assignment Model.Network Model.Waiting Model (queuing Theory).Probability.Theoretical Probability Distributions.Probability Distribution Of A Random Variable.Inventory Model.Game Theory.Simulation.
Here is the video about Linear Programming Problem using Big M method in Operations research, In this video we discussed what is big m method and how to solve this method easily using simple formulas, hope this will help you to get the subject knowledge at the end.