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

First, you may interpret a variable’s reduced cost as the amount that 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 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 units in a minimization model.

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