TWO-STAGE LINEAR PROGRAM UNDER UNCERTAINTY: A BASIC PROPERTY OF THE OPTIMAL SOLUTION.
Abstract
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1966
- Accession Number
- AD0630620
Entities
People
- Katta G. Murty