Optimal Policies for a Capacitated Two-Echelon Inventory System

Rodney P. Parker · Roman Kapuściński

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

Abstract

This paper demonstrates optimal policies for capacitated serial multiechelon production/inventory systems. Extending the Clark and Scarf (1960) model to include installations with production capacity limits, we demonstrate that a modified echelon base-stock policy is optimal in a two-stage system when there is a smaller capacity at the downstream facility. This is shown by decomposing the dynamic programming value function into value functions dependent upon individual echelon stock variables. We show that the optimal structure holds for both stationary and nonstationary stochastic customer demand. Finite-horizon and infinite-horizon results are included under discounted-cost and average-cost criteria.

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References

1960Optimal Policies for a Multi-Echelon Inventory Problem 2004Optimal Policies for a Multi-Echelon Inventory Problem 2002Foundations of Stochastic Inventory Theory 2000Stochastic Dynamic Programming and the Control of Queueing Systems 1986An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion 1984Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model 1989Optimal Inventory Policies for Assembly Systems Under Random Demands 1966The Status of Mathematical Inventory Theory

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2017Asymptotic Optimality of Tailored Base-Surge Policies in Dual-Sourcing Inventory Systems 2008Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity 2008A Single-Unit Decomposition Approach to Multiechelon Inventory Systems 2005Safety Stock Positioning in Supply Chains with Stochastic Lead Times 2004On Measuring Supplier Performance Under Vendor-Managed-Inventory Programs in Capacitated Supply Chains

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