The Computation of Shadow Prices in Linear Programming

The purpose of this paper is to demonstrate that when degeneracy is present in an optimal basic solution to a linear programming problem, the optimal values of the dual variables do not necessarily correspond to shadow prices. In such instances, major commercial L.P. packages (such as IBM's MPS and MPSX) may provide misleading information about the shadow prices. It will be shown how the actual values of the shadow prices may be determined, and the nature of the relationship between shadow prices and dual variables will be discussed.