Technical Note-Preservation of Additive Convexity and Its Applications in Stochastic Optimization Problems

• 成果类型: Article
• 署名作者: Gong, Xiting; Wang, Tong
• 署名单位: Chinese University of Hong Kong; Shanghai Jiao Tong University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2020.2064
• 发表日期: 2021
• 页码: 1015-1024
• 关键词: Inventory Management; optimal policies; assembly systems

摘要

In this paper, we establish two preservation results of additive convexity for a class of optimal transformation problems and a class of optimal disposal problems. For both classes of problems, there are multiple resources; our results show that if these resources have different priorities to be transformed/disposed under the optimal policy, then the additive convexity and bounded monotonicity of the objective function are preserved to the value function after optimization. A key observation is that an optimal transformation problem with prioritized optimal decisions is equivalent to a serial inventory problem with zero lead times. We demonstrate the applications of our results to several stochastic optimization problems in operations management.