Inventory Control for Spectrally Positive Levy Demand Processes

• 成果类型: Article
• 署名作者: Yamazaki, Kazutoshi
• 署名单位: Kansai University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0801
• 发表日期: 2017
• 页码: 212-237
• 关键词: optimal dividends problem; optimal stopping problems; smooth fit principle; diffusion demands; compound poisson; terminal value; optimality; ergodicity; management; american

摘要

A new approach to solve the continuous-time stochastic inventory problem using the fluctuation theory of Levy processes is developed. This approach involves the recent developments of the scale function that is capable of expressing many fluctuation identities of spectrally one-sided Levy processes. For the case with a fixed cost and a general spectrally positive Levy demand process, we show the optimality of an (s,S)-policy. The optimal policy and the value function are concisely expressed via the scale function. Numerical examples under a Levy process in the beta-family with jumps of infinite activity are provided to confirm the analytical results. Furthermore, the case with no fixed ordering costs is studied.