Approximate solutions for discrete stochastic optimization problems are often obtained via simulation. It is reasonable to complement these solutions by confidence regions for the argmin-set. We address the question, how a certain total number of random draws should be distributed among the set of alternatives. We propose a one-step allocation rule which turns out to be asymptotically optimal in the case of normal errors for two goals: To minimize the costs caused by using only an approximate solution and to minimize the expected size of the confidence sets
