Technical Note—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 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.