A Class of Stochastic Mathematical Programs with Correlated Scale Parameters in the Objective and Right-Hand Side

This note studies a class of stochastic programs with scale parameters in the objective function and right-hand side. Linear programs are an important special case of this class. The scale parameters are a pair of jointly distributed random variables. The basic issue addressed is the type of biases...

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Bibliographic Details
Published in:Operations research 1984-07, Vol.32 (4), p.945-951
Main Authors: Soyster, A. L., Foley, R. D., Murphy, F. H.
Format: Article
Language:English
Subjects:
Applied sciences
Covariance
Covariance matrices
Exact sciences and technology
Expected values
Linear programming
Mathematical independent variables
Mathematical models
Mathematical programming
Mathematical vectors
Objective functions
Operational research and scientific management
Operational research. Management science
Optimal solutions
Random variables
Scalars
Stochastic models
Technical Notes
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Summary:This note studies a class of stochastic programs with scale parameters in the objective function and right-hand side. Linear programs are an important special case of this class. The scale parameters are a pair of jointly distributed random variables. The basic issue addressed is the type of biases introduced by replacing the random variables by their expected values. As one would expect, the covariance between the random variables is of central importance. Depending upon the sign of the covariance, the objective value of the program, in which the random variables are replaced by their expected values, is greater or lesser than the expected objective function value of the stochastic program.
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.32.4.945