Stochastic Programs with Fixed Recourse: The Equivalent Deterministic Program

To each stochastic program corresponds an equivalent deterministic program. The purpose of this paper is to compile and extend the known properties for the equivalent deterministic program of a stochastic program with fixed recourse. After a brief discussion of the place of stochastic programming in the realm of stochastic optimization, the definition of the problem at hand, and the derivation of the deterministic equivalent problem, the question of feasibility is treated in § 4 with in § 5 a description of algorithmic procedures for finding feasible points and in § 6 a characterization of a special but important class of problems. Section 7 deals with the properties of the objective function of the deterministic equivalent problem, in particular with continuity, differentiability and convexity. Finally in § 8, we view the equivalent deterministic program in terms of its stability, dualizability and solvability properties.

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