Lesson plan
slack variable
In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality constraint. A non-negativity constraint on the slack variable is also added. Slack variables are used in particular in linear programming. As with the other variables in the augmented constraints, the slack variable cannot take on negative values, as the simplex algorithm requires them to be positive or zero. * If a slack variable associated with a constraint is zero at a particular candidate solution, the constraint is binding there, as the constraint restricts the possible changes from that point. * 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. Slack variables are also used in the Big M method.
Article summary
In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality constraint. A non-negativity constraint on the slack variable is also added. Slack variables are used in particular in linear programming. As with the other variables in the augmented constraints, the slack variable cannot take on negative values, as the simplex algorithm requires them to be positive or zero. * If a slack variable associated with a constraint is zero at a particular candidate solution, the constraint is binding there, as the constraint restricts the possible changes from that point. * 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. Slack variables are also used in the Big M method.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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