Notes on linear programming-part XLVIII: inequalities for stochastic linear programming problems.

by Albert Madansky

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A consideration of a linear-programming problem in which the "right-hand side" is a random vector whose expected value is known and where the expected value of the objective function is minimized. The conditions are studied under which an approximate solution (found by replacing the "right-hand side" by its expected value and solving the resulting linear programming problem) is satisfactory. In particular, conditions are given for the equality of the expected value of the objective function for the optimal solution and the value of the objective function for the approximate solution. Bounds on these values are also given. The relation is discussed between this problem and a related problem where an observation is made on the "right-hand side" and where the non- stochastic linear programming problem based on this observation is solved

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