Section] Section] Section] Section] Section] Section] Section] Section] Section] 0 Some Convexity and Sensitivity Properties of the (r, T) Inventory Control Policy for Stochastic Demand

We show that long-run average cost function for the (R, T) policy with normally distributed demand has a structure similar to that of the corresponding (Q, r) model so that many of the useful properties of the latter model are applicable. In particular, (i) the optimal cost is relatively insensitive to the choice of the reorder interval, T, provided a near-optimal R corresponding to the chosen T is used. (ii) The relative percentage increase in costs due to use of a suboptimal T obtained via a deterministic analysis is at most 6.125%. In addition we show that, (i) Use of an (R, T) policy instead of the optimal policy increases costs by at most 41.42%. (ii) In computational experiments, the (R, T) policy exhibits substantially superior insensitivity and near-optimality properties when compared to the above worst case guarantees. We also characterize certain problem instances for which the empirical performance of the (R, T) policy may be expected to deteriorate. (iii) Simple Power-of-Two, (R, T)-based heuristics for the multi-item joint replenishment problem and the single-item, two-stage serial system have a worst-case performance guarantee of 1.5 and 1.875 respectively.