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reduced cost
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.
Given a system minimize subject to , the reduced cost vector can be computed as , where is the dual cost vector.
It follows directly that for a minimization problem, any non-basic variables at their lower bounds with strictly negative reduced costs are eligible to enter that basis, while any basic variables must have a reduced cost that is exactly 0. 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.
== Interpretation ==
For the case where x and y are optimal, the reduced costs can help explain why variables attain the value they do. For each variable, the corresponding sum of that stuff gives the reduced cost show which constraints forces the variable up and down. For non-basic variables, the distance to zero gives the minimal change in the object coefficient to change the solution vector x.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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