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Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs
Author(s) -
Presman Ernst,
Sethi Suresh P.
Publication year - 2006
Publication title -
production and operations management
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.279
H-Index - 110
eISSN - 1937-5956
pISSN - 1059-1478
DOI - 10.1111/j.1937-5956.2006.tb00245.x
Subject(s) - poisson distribution , economic order quantity , constant (computer programming) , mathematical optimization , regular polygon , component (thermodynamics) , function (biology) , computer science , task (project management) , mathematical economics , economics , econometrics , mathematics , statistics , supply chain , physics , geometry , management , evolutionary biology , biology , political science , law , thermodynamics , programming language
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.