This paper considers a single-item, periodic review inventory model with uncertain demands. We assume a finite production capacity in each period. With stationary data, a convex one-period cost function and a continuous demand distribution, we show (under a few additional unrestrictive assumptions) that a modified basic-stock policy is optimal under the discounted cost criterion, both for finite and infinite planning horizons. In addition we characterize the optimal base-stock levels in several ways.
Federgruen, Awi, and Paul Zipkin. "An inventory model with limited production capacity and uncertain demands II: The discounted-cost criterion." Mathematics of Operations Research 11, no. 2 (May 1986): 208-215.
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