Capacitated inventory problems with fixed order costs: Some optimal policy structure

Guillermo Gallego · Alan Andrew Scheller-Wolf

89 citations0/0 files storedEuropean Journal of Operational Research

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Supply Chain and Inventory Management Management and Optimization Techniques Optimization and Search Problems

Abstract

Almost 40 years ago, H. Scarf (The optimality of (s,S) policies in dynamic inventory problems, in: K. Arrow, S. Karlin, P. Suppes (Eds.), Mathematical Models in the Social Sciences, Stanford University Press, Stanford, 1960) established the optimal (s,S) policy structure for the periodic review inventory problem with fixed ordering costs and no capacity constraint. Since then, the capacitated problem has resisted characterization. In the present paper we partially bridge this gap; using a generalization of Scarf's K-convexity we show that the optimal capacitated policy has an (s,S)-like structure. To do so we divide the parameter space into four regions: In two of these regions the optimal policy is completely specified, while in the other two, it is partially specified. We complement these findings with a computational study. This study suggests that a still simpler optimal policy structure exists.

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References

1951Optimal Inventory Policy 2005The Optimality of (S,s) Policies in the Dynamic Inventory Problem 1963Mathematical Models in the Social Sciences 1986An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion 1986An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion 1991A simple proof for optimality of (s, S) policies in infinite-horizon inventory systems

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