对偶线性规划基解不对称性产生的矛盾和影子价格确定

The Contradiction Created by the Nonsymmetry of the Dual Linear Programming and Ascertainment of the Shadow Price

互为对偶的两个线性规划问题中,当基解不是一一对应时,就会产生矛盾:退化基不一定对偶退化;可行基不一定对偶可行;最优基不一定对偶最优.这对影子价格确定有重要影响,会出现多影子价格和无界影子价格问题.

As far as the two problems in linear programming of mutual dualityare concerned, the non-correspondence of the basic relation will result in contradictions： degenerate base does not necessarily degenerate in duality; feasible base may not be feasible in duality; the optimum base may not be optimal in duality. Those contradictions will greatly influence the ascertainment of the resources price, from which multi-shadow price and unbounded shadow price may arise.