Technical Note-Asymptotically Optimal Control of Omnichannel Service Systems with Pick-up Guarantees

• 成果类型: Article
• 署名作者: Gao, Xuefeng; Huang, Junfei; Zhang, Jiheng
• 署名单位: Chinese University of Hong Kong; Chinese University of Hong Kong; Hong Kong University of Science & Technology
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2416
• 发表日期: 2024
• 页码: 1739-1748
• 关键词: strategic idleness; CUSTOMER

摘要

Motivated by the recent popularity of omnichannel service systems, we analyze the joint admission and scheduling control of a queueing system with two classes of customers: online and walk-in. Unlike walk-in customers, online customers are given a target time for pick up upon placing an order. Thus, in addition to minimizing the waiting costs of walk-in customers and the rejection cost of both classes, we need to minimize the earliness and tardiness costs of online customers. Such a distinctive objective makes the control problem difficult to analyze. We develop a novel analysis by adopting the idea of proving H = lambda G to establish an asymptotic relationship between the waiting time cost and the queue length cost under general control policies in the heavy-traffic regime. We also design a policy and show that it is asymptotically optimal.