Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times

• 成果类型: Article
• 署名作者: Goldberg, David A.; Katz-Rogozhnikov, Dmitriy A.; Lu, Yingdong; Sharma, Mayank; Squillante, Mark S.
• 署名单位: University System of Georgia; Georgia Institute of Technology; International Business Machines (IBM); IBM USA; International Business Machines (IBM); IBM USA
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0760
• 发表日期: 2016
• 页码: 898-913
• 关键词: approximation scheme; period; SYSTEM

摘要

Lost sales inventory models with large lead times, which arise in many practical settings, are notoriously difficult to optimize due to the curse of dimensionality. In this paper, we show that when lead times are large, a very simple constant-order policy, first studied by Reiman, performs nearly optimally. The main insight of our work is that when the lead time is very large, such a significant amount of randomness is injected into the system between when an order for more inventory is placed and when the order is received, that being smart algorithmically provides almost no benefit. Our main proof technique combines a novel coupling for suprema of random walks with arguments from queueing theory.