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Information delays exist when the most recent inventory information available to the Inventory Manager (IM) is dated. In other words, the IM observes only the inventory level that belongs to an earlier period. Such situations are not uncommon, and they arise when it takes a while to process the demand data and pass the results to the IM. In this paper, we establish that the average cost optimal policy is of state-dependent basestock type with respect to the reference inventory position. We show that the optimal base stock depends on the age and the magnitude of the latest observed delay. We illustrate the results by solving an example with delays of 0 and 1, for which we are able to obtain formulas/bounds for the basestock levels.