The paper considers a stochastic inventory control system consisting of a central store (CS) and several lower stores (LS). The demand at each of the lower stores forms a recurrent stochastic flow. To replenish the stock the LS's file orders of fixed quantity with the CS following a two‐level control policy. In its turn, the CS also orders replenishments, and all the lots are delivered to it with some fixed delay. The orders from an LS to the CS are fulfilled in a delivery time if the lot required is in stock at the CS, otherwise the CS must itself wait for replenishment before sending the lot to the LS. The main result obtained is an approximate formula for the probability of the smooth operation of such a system.
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