Abstract
A method is proposed for finding a closed form expression for the cumulative distribution function (CDF) of the maximum value of the objective function in a stochastic linear programming problem in the case where either the objective function coefficients or the right-hand side coefficients are given by known probability distributions. If the objective function coefficients are random, the CDF is obtained by integrating over the space for which a given feasible basis remains optimal. A transformation is presented using the Jacobian theorem which simplifies the regions of integration and often simplifies the integration itself. A similar analysis is presented in the case where the right-hand side coefficients are random. An example is given to illustrate the technique.
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