In this paper we study Make-To-Stock manufacturing systems and generalize the results obtained in Panayiotou et al. (2002). Specifically, we use the same modeling framework to derive sample derivatives of the objective function of interest with respect to buffer capacities (hedging points). In the earlier work, the input processes (machine processing and demand) were assumed piecewise constant. In this work, we generalize the results to piecewise differentiable processes. The derived estimates are unbiased and non-parametric, in the sense that they require no knowledge of the distributions of the underlying random processes. However, unlike the earlier results, these estimators require knowledge of some rates at certain points in time.
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