Technical Note-Production Management with General Demands and Lost Sales

• 成果类型: Article
• 署名作者: Han, Jinhui; Li, Xiaolong; Sethi, Suresh P.; Siu, Chi Chung; Yam, Sheung Chi Phillip
• 署名单位: Peking University; University of Hong Kong; University of Texas System; University of Texas Dallas; Hang Seng University of Hong Kong; Chinese University of Hong Kong
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.0191
• 发表日期: 2024
• 页码: 1750-1764
• 关键词: production-inventory system; optimal replenishment rate; lost sales; Le ' vy subordinator; Fourier-cosine method; risk analytics

摘要

We consider continuous -review, single -product inventory systems with a constant replenishment rate, Levy demand, general inventory holding cost, and general lostsales penalty. The Levy demand encompasses various demand dynamics used in the inventory literature. We obtain optimal replenishment rates that minimize the timeaverage cost and expected discounted costs. We can solve this problem explicitly for the optimal replenishment rate by utilizing the renewal theorem for the time -average cost objective. For a more complex expected discounted cost minimization problem, we first obtain the Laplace transform of the cost objective in terms of the unique positive root of the corresponding Lundberg equation. Then, we devise a Fourier -cosine scheme to numerically compute the original cost objective together with a detailed error analysis to determine the optimal production rate. In particular cases, we obtain closed -form expressions of the optimal replenishment rates. The numerical examples further illustrate our numerical method's accuracy, stability, and robustness. Finally, our Fourier -cosine method can be applied to compute risk analytics, including but not limited to the stockout probability and expected shortfall of the production -inventory system.