Expected Objective Value of a Stochastic Linear Program and the Degree of Uncertainty of Parameters

In this paper, we characterize the relationship between the expected optimal value of a stochastic linear program and a stochastic program with recourse and the degree of uncertainty in the objective function coefficients c and the stipulation vector b. It is shown that under certain conditions the expected objective value is nondecreasing as the degree of uncertainty in c increases and the opposite is true for the case of b. The degree of uncertainty of a random vector is defined in terms of a covariance matrix. Some managerial interpretations are also given.