Inventory models with continuous and Poisson demands and discounted and average costs

Inventory models with continuous and Poisson demands and discounted and average costs

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Article ID: iaor20071098
Country: United States
Volume: 15
Issue: 2
Start Page Number: 279
End Page Number: 293
Publication Date: Jan 2006
Journal: Production and Operations Management
Authors: ,
Keywords: economic order
Abstract:

We develop a new, unified approach to treating continuous-time stochastic inventory problems with both the average and discounted cost criteria. The approach involves the development of an adjusted discounted cycle cost formula, which has an appealing intuitive interpretation. We show for the first time that an (s, S) policy is optimal in the case of demand having a compound Poisson component as well as a constant rate component. Our demand structure simultaneously generalizes the classical EOQ model and the inventory models with Poisson demand, and we indicate the reasons why this task has been a difficult one. We do not require the surplus cost function to be convex or quasi-convex as has been assumed in the literature. Finally, we show that the optimal s is unique, but we do not know if optimal S is unique.

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