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.