In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality. Introducing a slack variable replaces an inequality constraint with an equality constraint and a non-negativity constraint on the slack variable. What is meant by surplus variable?
So, what is slack Slack and artificial variable?
Slack variable: It is used o convert a Less than or equal to (≤) constraint into equality to write standard form. Surplus & Artificial variables: They are used to convert Greater than or equal to (≥) constraint into equality to write standard form. Keeping this in consideration, what is slack and surplus variable?
If a slack variable is positive at a particular candidate solution, the constraint is non-binding there, as the constraint does not restrict the possible changes from that point. If a slack variable is negative at some point, the point is infeasible (not allowed), as it does not satisfy the constraint.
What are slack and surplus variables in LPP?
Slack and surplus variables are used for the purpose of solving Linear Programming Problems (LPP). The variable is added to the constraints when it is in the less than or equal constraints whereas, the surplus variables are applies for the greater or equal constraints (Anderson, et al, 2015).
What is the difference between Slack and surplus?
The term “slack” applies to less than or equal constraints, and the term “surplus” applies to greater than or equal constraints. If a constraint is binding, then the corresponding slack or surplus value will equal zero.
What is slack and surplus in economics?
The variable s is called a slack variable because it measures the amount of slack ( idle ) resources still remaining in stock at any point in time during the production process. Since it is not possible to have negative slack, nonnegativity constraints also apply to slack variables.
What is the slack or surplus value of a binding constraint?
If a constraint is binding, then the corresponding slack or surplus value will equal zero. Question is, what is a surplus variable? A surplus variable refers to the amount by which the values of the solution exceeds the resources utilized.