Abstract
This paper studies the behavior of the optimum value of a two-stage stochastic program with recourse (random right-hand sides) as the mean and covariance matrices defining the random variables in the program are perturbed. Several results for convex programs are developed and are used to study the effect such perturbations have on the regularity properties of the stochastic programs. Cost associated with incorrectly specifying the mean and covariance matrices are discussed and estimated. A stochastic programming model in which the random variable is dependent on the first-stage decision is presented.
Similar content being viewed by others
References
S.J. Garstka, “Stochastic programs with recourse: Random recourse costs only”,Management Science 19 (1973) 747–750.
S.J. Garstka, “Regularity conditions for a class of convex programs”,Management Science 20 (1973) 373–377.
C.R. Rao,Linear statistical inference and its application (Wiley, New York, 1965).
R. Van Slyke and R. Wets, “L-shaped linear programs with applications to optimal control and stochastic linear programming”,SIAM Journal on Applied Mathematics 17 (1969) 638–663.
D.W. Walkup and R. Wets, “Stochastic programs with recourse”,SIAM Journal on Applied Mathematics 15 (1967) 1299–1314.
D.W. Walkup and R. Wets, “Some practical regularity conditions for nonlinear programs”,SIAM Journal on Control 7 (1969) 430–436.
R. Wets, “Characterization theorems for stochastic programs”,Mathematical Programming 2 (1972) 166–175.
R. Wets, “Stochastic programs with fixed recourse: The equivalent deterministic program”, Manuscript, University of Kentucky, Lexington, Ky. (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Garstka, S.J. Distribution functions in stochastic programs with recourse: A parametric analysis. Mathematical Programming 6, 339–351 (1974). https://doi.org/10.1007/BF01580249
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01580249