This paper examines a constrained stochastic inventory optimization problem by means of sample average approximations (SAA). The problem is formulated based on the lead time demand parameters. Lead time demands are sampled by a bootstrap method that is performed by randomly generating demand values over deterministic lead time values. In order to increase the efficiency of solving an SAA replication, a number of variance reduction techniques (VRT) are proposed, namely: antithetic variates,

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... n random numbers and Latin hypercube sampling methods. A set of experiments investigates the quality of these VRTs on the estimated optimality gap and gap variance results for different demand processes. The results indicate that the use of VRTs produces significant improvements over the crude Monte Carlo sampling method on all test cases.