Abstract
We consider a discrete review, single product, dynamic inventory model, in which the demand process is related to an environmental process. Sufficient conditions are found for the optimality of a $(z,Z)$-order-policy: whenever the environmental process is in state $i \in I$, order up to $Z(i)$, if the stock is less than $z(i)$, and do not order, otherwise. Moreover, bounds are given for the critical numbers $z(i)$, $Z(i)$, of an optimal $(z,Z)$-order-policy.
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