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Solving Discrete Optimization Problems When Element Costs are Random

In a general class of discrete optimization problems with min-sum objective function, some of the elements may have random costs associated with them. In such a situation, the notion of optimality needs to be suitably modified. We define an optimal solution to be a feasible solution with the minimum risk. It is shown that the knowledge of the means of these random costs is enough to reduce such a problem into one with no random costs.