STOCHASTIC PROGRAMS WITH RECOURSE.
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
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So far the study of stochastic programs with recourse has been limited to the case called by G. Dantzig programming under uncertainty when only the right-hand sides or resources of the problem are random. In this paper the authors extend the theory to the general case when essentially all the parameters involved are random. This generalization immediately raises the problem of attributing a precise meaning to the stochastic constraints. They examine a probability formulation satisfying the constraints almost surely and a possibility formulation satisfying the constraints for all values of the random parameters in the support of their joint distribution and show them equivalent under a rather weak but curious W-condition. Finally, they prove that without restriction the equivalent deterministic form of a stochastic program with recourse is a convex program for which we obtain some additional properties when some of the parameters of the original problem are constant. The applications of the theoretical results of this paper to certain classes of stochastic programs which have arisen from practical problems will be presented in a separate paper Stochastic Programs with Recourse Special Forms. Author
- Operations Research