In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase for maximization problem, decrease for minimization problem) before it would be possible for a corresponding variable to assume a positive value in the optimal solution.
It is the cost for increasing a variable by a small amount, i.e., the first derivative from a certain point on the polyhedron that constrains the problem.
When the point is a vertex in the polyhedron, the variable with the most extreme cost, negatively for minimization and positively maximization, is sometimes referred to as the steepest edge.
For a maximization problem, the non-basic variables at their lower bounds that are eligible for entering the basis have a strictly positive reduced cost.
For the case where x and y are optimal, the reduced costs can help explain why variables attain the value they do.
In principle, a good pivot strategy would be to select whichever variable has the greatest reduced cost.
The Devex algorithm attempts to overcome the latter problem by estimating the reduced costs rather than calculating them at every pivot step, exploiting that a pivot step might not alter the reduced costs of all variables dramatically.
NOTE: This is a direct quote from the web site linked below: "Associated with each variable is a reduced cost value.
In this case, where, for example, the objective function coefficient might represent the net profit per unit of the activity.