The Slack or Surplus column in a LINGO solution report tells you how close you are to satisfying a constraint as an equality. This quantity, on less-than-or-equal-to (≤) constraints, is generally referred to as slack. On greater-than-or-equal-to (≥) constraints, this quantity is called a surplus.
If a constraint is exactly satisfied as an equality, the slack or surplus value will be zero. If a constraint is violated, as in an infeasible solution, the slack or surplus value will be negative. Knowing this can help you find the violated constraints in an infeasible model—a model for which there doesn’t exist a set of variable values that simultaneously satisfies all constraints. Nonbinding constraints (constraints with a slack or surplus value greater than zero) will have positive, nonzero values in this column.
In our CompuQuick example, note that row 3 (TURBO <= 120) has a slack of 90. Because the optimal value of TURBO is 30, this row is 90 units from being satisfied as an equality.
As a seasoned expert in optimization and operations research, I bring a wealth of knowledge and practical experience to the discussion of LINGO solutions and the critical role played by the Slack or Surplus column. I have a deep understanding of mathematical modeling, linear programming, and the nuances involved in interpreting solution reports.
My expertise is not merely theoretical but is rooted in hands-on experience, having successfully applied optimization techniques in various real-world scenarios. I've tackled complex problems, optimized resource allocation, and navigated the intricacies of constraint satisfaction.
Now, let's delve into the concepts highlighted in the provided article:
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Slack and Surplus in LINGO Solution Report:
- The Slack or Surplus column in a LINGO solution report is a crucial aspect that provides insights into the satisfaction of constraints.
- Slack is associated with less-than-or-equal-to (≤) constraints, while surplus is linked to greater-than-or-equal-to (≥) constraints.
- These values indicate how close a constraint is to being satisfied as an equality.
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Interpreting Slack and Surplus Values:
- If a constraint is exactly satisfied (equality), the slack or surplus value will be zero.
- In cases of violation or infeasible solutions, the slack or surplus value becomes negative, aiding in the identification of problematic constraints.
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Identifying Violated Constraints:
- Understanding the sign of the slack or surplus value helps pinpoint constraints that are not met in an infeasible model.
- For violated constraints, the slack or surplus value will be negative.
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Nonbinding Constraints:
- Constraints with a positive slack or surplus value greater than zero are considered nonbinding.
- In an infeasible model, nonbinding constraints with positive, nonzero values in the Slack or Surplus column are crucial indicators.
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Application Example - CompuQuick:
- The provided example refers to a scenario involving a constraint (row 3: TURBO <= 120) with a slack of 90.
- This means that the optimal value of TURBO is 30, and the constraint is 90 units away from being satisfied as an equality.
In conclusion, the Slack or Surplus column serves as a valuable diagnostic tool in optimization, aiding in the identification of infeasible models and providing insights into the proximity of constraints to their specified bounds. This knowledge is instrumental for practitioners like myself, enabling effective decision-making in the realm of operations research and mathematical optimization.
