Stochastic Inventory Models with Limited Production Capacity and Periodically Varying Parameters

Yossi Aviv · Awi Federgruen

79 citations0/0 files storedProbability in the Engineering and Informational Sciences

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Supply Chain and Inventory Management Management and Optimization Techniques Advanced Queuing Theory Analysis

Abstract

We consider a single-item, periodic-review inventory model with uncertain demands in which each period's production volume is limited by a capacity level. The demand distributions, capacity levels, and cost parameters vary according to a periodic pattern. We prove that modified base-stock policies are optimal for the finite-horizon planning model and for both the infinite-horizon discounted and undiscounted cost criterion. We further show that the optimal base-stock levels can be calculated via a simple but efficient value-iteration method. Finally, we have conducted a comprehensive numerical study to ascertain the efficiency of this solution method as well as various qualitative properties of the performance of capacitated production/inventory systems under periodically varying demand and cost patterns.

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References

1987Applied Probability and Queues 1993Inventory Control in a Fluctuating Demand Environment 1986An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion 1960Dynamic Inventory Policy with Varying Stochastic Demands 1995Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems 1986An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion 1998A Capacitated Production-Inventory Model with Periodic Demand 1991Production Smoothing Evidence from Physical-Product Data

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