LINGO is a simple tool which lets you utilize the power of linear and nonlinear optimization to formulate large problems conci

Summary statistic

The first few lines of the solution report contain a number of summary statistics concerning the model.

The first line consists of:

the number of rows (i.e., constraints) in the model (4),

the number of variables (2),

the number of integer variables (0), with the number that are 0/1 (i.e., binary) in parentheses.

The second line contains:

the number of nonzero coefficients in the whole model (9),

the number of nonzero coefficients in the constraints (4), with the number that are +1 or -1 in parentheses (3 are +- 1),

Model density (0.75), defined as: (number of nonzeros)/[(number of rows) * (number of columns +1)].

Line three consists of the absolute values of the smallest and largest nonzeros in the model respectively (1 160).

The fourth line consists of:

the number of less than or equal to, equality, and greater than or equal to constraints in the model (3, 0, 0),

the sense of the objective function (MAX),

the upper bound estimate of the number of generalized upper bound (GUBS) constraints in the modelconstraints which have no variable in common (2).

Reduced cost

In a LINGO solution report, youll find a reduced cost figure for each variable. There are two valid, equivalent interpretations of a reduced cost.

First, you may interpret a variables reduced cost as the amount by which the objective coefficient of the variable would have to improve before it would become profitable to give the variable in question a positive value in the optimal solution. For example, if a variable had a reduced cost of 10, the objective coefficient of that variable would have to increase by 10 units in a maximization problem and/or decrease by 10 units in a minimization problem in order for the variable to become an attractive alternative to enter into the solution. A variable in the optimal solution, as in the case of STANDARD or TURBO, automatically has a reduced cost of zero.

Second, the reduced cost of a variable may be interpreted as the amount of penalty you would have to pay to introduce one unit of that variable into the solution. Again, if you have a variable with a reduced cost of 10, you would have to pay a penalty of 10 units to introduce the variable into the solution. In other words, the objective value would fall by 10 units in a maximization model or increase by 10 in a minimization.

Reduced costs are valid only over a range of values. For more information on determining the valid range of a reduced cost, see the Range command in Windows Commands .

Slack or surplus

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 () constraints, is generally referred to as slack. On greater than or equal () 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 modela model for which there exists no set of variable values which simultaneously satisfies all constraints. Non-binding 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