Properties of the Periodic Review (R, T) Inventory Control Policy for Stationary, Stochastic Demand

This paper compares the commonly used periodic review, replenishment interval, order-up-to (R, T ) policy to the continuous review, reorder point, order quantity, (Q, r) model. We show that long-run average cost function for the single-product (R, T ) policy has a structure similar to that of the (Q, r) model. Consequently, many of the useful properties of the latter model are applicable. In particular, the optimal cost is insensitive to the choice of the replenishment interval, T, provided the optimal order-up-to level, R, corresponding to T is used. For instance, a suboptimal T obtained from a deterministic analysis increases costs by no more than 6.125%. For continuous demand, we analytically prove that use of a (R, T)policy instead of the optimal policy increases costs by at most 41.42% in the worst case. Computational experiments on Poisson demand demonstrate that the average-case relative error of using a (R,T)policy is under 7.5%. This relative error is lower when the demand rate and leadtime are high and the fixed order costs are either very low or very high. When coordination of order placement epochs is desirable, the (R,T) policy may sometimes be preferred to the (Q, r) policy. In this context, we illustrate application of our single-product results to more complex systems. In particular, we show that a simple power-of-two, (R,T) based heuristic for the stochastic multiproduct joint replenishment problem has a worst-case performance guarantee of 1.5. A similar result is explored for a special case of a two-echelon serial inventory system