An inventory model with limited production capacity and uncertain demands. II: The discounted-cost criterion.

*(English)*Zbl 0628.90017[For the first part see ibid. 11, 193-207 (1986; Zbl 0602.90053).]

This paper is the second part of the authors’ work on periodic review inventory models with finite production capacity and uncertain demands. The first part considered the discrete demand average cost criterion, while this now studies the continuous demand expected discounted cost criterion.

The authors set out to prove the optimality under the discounted cost criterion of a stationary modified base-stock policy characterized by a single critical value. If the stock is below it, then production is designed to raise the stock towards its critical value; if otherwise, no production is initiated. The method used in the proof of the main Theorem is based on the limiting behavior of the sequence of finite planning horizon problems, and the authors show that the optimal base-stock level and optimal cost function are limits of their finite horizon counterparts. The paper concludes by obtaining the expected cost of modified base-stock policies, and hence characterizing optimal base-stock levels, at least partially.

This paper is the second part of the authors’ work on periodic review inventory models with finite production capacity and uncertain demands. The first part considered the discrete demand average cost criterion, while this now studies the continuous demand expected discounted cost criterion.

The authors set out to prove the optimality under the discounted cost criterion of a stationary modified base-stock policy characterized by a single critical value. If the stock is below it, then production is designed to raise the stock towards its critical value; if otherwise, no production is initiated. The method used in the proof of the main Theorem is based on the limiting behavior of the sequence of finite planning horizon problems, and the authors show that the optimal base-stock level and optimal cost function are limits of their finite horizon counterparts. The paper concludes by obtaining the expected cost of modified base-stock policies, and hence characterizing optimal base-stock levels, at least partially.

Reviewer: J.M.Gani

##### MSC:

90B05 | Inventory, storage, reservoirs |