TWO-STAGE LINEAR PROGRAM UNDER UNCERTAINTY: A BASIC PROPERTY OF THE OPTIMAL SOLUTION.
OPERATIONS RESEARCH CENTER UNIV OF CALIF BERKELEY
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The two-stage linear program under uncertainty proposed by George B. Dantzig and developed by A. Madansky, A. Williams, Roger Wets and R. Van Slyke is considered. Roger Wets has shown that the set of feasible solutions to a linear program under uncertainty is a convex polyhedron, and the objective function to be minimized is a convex function. In this paper the author shows that there exists an optimal solution to the linear program under uncertainty in which the column vectors corresponding to the positive first-stage decision variables are linearly independent. This leads to the result that there exists an optimal solution in which not more than m m bar of the first-stage decision variables are positive. Author
- Operations Research