Research Article Some Properties of Multiple Parameters Linear Programming

Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function f can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of f at any point can be computed by solving a linear programming problemwhen only an optimal solution is available at the point. 1