The Precise Management Meaning of a Shadow Price

A shadow price of a resource constraint in linear programming is usually defined as the maximum price which should be paid to obtain an additional unit of resource. This definition, however, is imprecise and could lead to incorrect decisions. Because a shadow price already incorporates variable costs involved in the addition of the extra resource unit, shadow price should be defined as the maximum permissible amount of those costs involved in the addition which have not been included in the per-unit contributions of the basic decision variables. This note provides the precise meaning of a shadow price, together with examples of its use in a decision context.