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

*(English)*Zbl 0602.90053This paper is concerned with a production model in which a single item is controlled under periodic review. Linear production cost is calculated at the beginning of each period, and a convex function represents expected penalty and holding costs at the end of the period. Demand in each period is discrete, nonnegative and independent of demands in other periods, all data being stationary, with the planning horizon infinite. The paper’s main difference with previous work in this area is that production capacity is now considered to be finite in each period.

It is shown that a modified base-stock policy is optimal under the average cost criterion, and the optimal base-stock level is characterized. An optimality proof for finite inventory capacity is given, and it is shown that the same policy is optimal for infinite capacity under a slight restriction of the policy space.

It is shown that a modified base-stock policy is optimal under the average cost criterion, and the optimal base-stock level is characterized. An optimality proof for finite inventory capacity is given, and it is shown that the same policy is optimal for infinite capacity under a slight restriction of the policy space.

Reviewer: J.M.Gani

##### MSC:

90B05 | Inventory, storage, reservoirs |

60K30 | Applications of queueing theory (congestion, allocation, storage, traffic, etc.) |

90B30 | Production models |