This paper considers a single-item, periodic-review inventory model with uncertain demands. In contrast to prior treatments of this problem we assume a finite production capacity per period. Assuming stationary data, a convex one-period cost function and a discrete demand distribution, we show (under a few additional unrestrictive assumptions) that a modified base-stock policy is optimal under the average-cost criterion; in addition, we characterize the optimal base-stock level.
Federgruen, Awi, and P. Zipkin. "An inventory model with limited production capacity and uncertain demands I: The average-cost criterion." Mathematics of Operations Research 11, no. 2 (May 1986): 193-207.
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