An inventory control model in which the state of the system is reviewed only at discrete, equally spaced time intervals is studied. A procurement is made if at the review period the inventory position of the system is less than or equal to a number k. The quantity procured is an integral multiple of a number Q. The total expected cost of review, procurement, holding inventory, and stockouts is determined under the assumption that all demands are ultimately met. The cost of a stockout is taken to consist of a fixed cost per unit out of stock plus a variable cost which is proportional to the time out of stock. Specific expressions for all the cost expressions are found for the case of 1 Poisson demands and fixed lead times, and 2 Poisson demands and gamma lead times. It is shown that many of the inventory models discussed in the literature are special cases of the model here described.
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