Abstract
We study a single product inventory system with nonnegative setup cost in which the demand is a continuous random variable but orders are restricted to be integer valued. Optimal policies, when there are no setup costs, have a nice form. However, we show that, when the setup costs are nonzero, optimal policies may have a very counterintuitive form without any particular structure. We obtain a bound for the increase in costs resulting from the restriction of orders to be integers and define a suboptimal policy whose performance is within that bound.
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