Difference between Slack, Surplus and Artificial variables | Slack vs. Surplus vs. Artificial Variables
Slack Variables :
Slack variable represents an unused quaintly of resources ; it is added to less than or equal (<) to type constraints in order to get an equality constraint.
Surplus Variables :
A surplus variable represents the amount by which solution values exceed a resource. These variables are also called ‘Negative Slack Variables’ . Surplus variables like slack variables carry a zero coefficient in the objective function. it is added to greater than or equal to (>) type constraints in order to get an equality constraint.
Artificial Variables :
Artificial variables are added to those constraints with equality (=) and greater than or equal to ( > ) sign. An Artificial variable is added to the constraints to get an initial solution to an LP problem. Artificial variables have no meaning in a physical sense and are not only used as a tool for generating an initial solution to an LP problem.
Particulars |
Slack Variable |
Surplus Variable |
Artificial Variable |
Mean |
Unused resources of the idle resources. |
Excess amount of resources utilized. |
No physical or economic meaning. It is Fictitious. |
When used ? |
With < Constraints |
With > Constraints |
With > And = constraints |
Coefficient |
+1 |
-1 |
+1 |
Co-efficient in the Z – objective function |
0 |
0 |
-M for Maximization and +M for minimization |
As Initial Program variable |
Used as starting point. |
Can’t be used since unit matrix condition is not satisfied |
It is initially used but later on eliminated. |
In Optimal Table |
Used to help for interpreting idle & key resources. |
– |
It indicates the Infeasible Solution |