Technical Note—Asymptotically Optimal Control of Omnichannel Service Systems with Pick-up Guarantees
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AbstractMotivated 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 = λG, 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.
Acceptance Date23/11/2022
All Author(s) ListXuefeng Gao, Junfei Huang, Jiheng Zhang
Journal nameOperations Research
Year2024
Month7
Volume Number72
Issue Number4
PublisherINFORMS
Pages1739 - 1748
ISSN0030-364X
eISSN1526-5463
LanguagesEnglish-United States

Last updated on 2024-20-08 at 00:37