In this article the authors apply perturbation analysis, combined with conditional Monte Carlo, to obtain derivative estimators of the expected cost per period with respect to s and S, for a class of periodic review (s,S) inventory systems with full backlogging, linear holding and shortage costs, and where the arrivals of demands follow a renewal process. They first develop the general form of four different estimators of the gradient for the finite-horizon case, and prove that they are unbiased. The authors next consider the problem of implementing the present estimators, and develop efficient methodologies for the infinite-horizon case. For the case of exponentially distributed demand interarrival times, they implement the estimators using a single sample path. Generally distributed interarrival times are modeled as phase-type distributions, and the implementation of this more general case requires a number of additional off-line simulations. The resulting estimators are still efficient and practical, provided that the number of phases is not too large. The authors conclude by reporting the results of simulation experiments. The results provide further validity of the present methodology and also indicate that the estimators have very low variance.
