On the Equivalence of Some Inventory Systems

In an earlier paper (“Some Models of Inventory and an Application”, Management Science, Vol. 2, No. 4, July, 1956) the author analyzed four inventory systems which were referred to as Models I, II, III, IV. In the present paper the notion of equivalence of inventory systems is introduced and it is shown that Models I and II are equivalent and so are models III and IV. The results are also extended to systems with non-zero leadtime. In all cases considered it is shown that the total expected costs of the systems (with or without leadtime) can be expressed in the form