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

• 成果类型: Article
• 署名作者: Presman, Ernst; Sethi, Suresh P.
• 署名单位: Russian Academy of Sciences; Central Economics & Mathematics Institute RAS; University of Texas System; University of Texas Dallas
• 刊物名称: PRODUCTION AND OPERATIONS MANAGEMENT
• ISSN/ISSBN: 1059-1478
• 发表日期: 2006
• 页码: 279-293
• 关键词: (s; S) policy; stochastic inventory model; EOQ model; compound Poisson process; average discounted-cost formula

摘要

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.