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

Xuefeng Gao (), Junfei Huang () and Jiheng Zhang ()
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Xuefeng Gao: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong SAR, China
Junfei Huang: Department of Decision Sciences and Managerial Economics, CUHK Business School, The Chinese University of Hong Kong, Hong Kong SAR, China
Jiheng Zhang: Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology, Hong Kong SAR, China

Operations Research, 2024, vol. 72, issue 4, 1739-1748

Abstract: 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 = λ 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.

Keywords: Stochastic Models; omnichannel service; heavy traffic; earliness and tardiness costs; asymptotically optimal control (search for similar items in EconPapers)
Date: 2024
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