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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xuefeng Gao & Junfei Huang & Jiheng Zhang, 2024. "Technical Note—Asymptotically Optimal Control of Omnichannel Service Systems with Pick-up Guarantees," Operations Research, INFORMS, vol. 72(4), pages 1739-1748, July.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:4:p:1739-1748
    DOI: 10.1287/opre.2022.2416
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