Technical Note-Average Cost Optimality in Partially Observable Lost-Sales Inventory Systems

• 成果类型: Article
• 署名作者: Bai, Xingyu; Chen, Xin; Stolyar, Alexander L.
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2305
• 发表日期: 2023
• 关键词: Markov decision process; average cost; optimality inequality; partial observations; lost sales

摘要

We consider a partially observable lost-sales inventory system, in which the inventory level is observed only when it reaches zero. We use the vanishing discount factor approach to prove the existence of a stationary optimal policy for the average cost minimization. As our main methodological contribution, we provide a way to verify the key condition of the vanishing discount factor approach???the uniform boundedness of the relative discounted value function. To accomplish that, we construct a valid policy, which, in a certain sense, ???copies??? the actions of another policy for the process with a different initial state. To the best of our knowledge, this paper is the first one on partially observable inventory models under the average cost criterion.