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  • Optimal Routing Under Deman...
    Chen, Jinsheng; Dong, Jing; Shi, Pengyi

    Operations research, 09/2023
    Journal Article

    When having access to demand forecasts, a crucial question is how to effectively use this information to make better resource allocation decisions, especially during demand surges like the COVID-19 pandemic. Despite the emergence of various advanced prediction models for hospital resources, there has been a lack of prescriptive solutions for hospital managers seeking concrete decision support, for example, guidance on whether to allocate beds from other specialties to meet the surge demand from COVID-19 patients by postponing elective surgeries. In their paper “Optimal Routing under Demand Surge: the Value of Future Arrival Rate,” the authors present a systematic framework to incorporate future demand into routing decisions in parallel server systems with partial flexibility and quantify the benefits of doing so. They propose a simple and interpretable two-stage index-based policy that explicitly incorporates demand forecasts into real-time routing decisions. Their analytical and numerical results demonstrate the policy’s effectiveness, even in the presence of large prediction errors. Motivated by the growing availability of advanced demand forecast tools, we study how to use future demand information in designing routing strategies in queueing systems under demand surges. We consider a parallel server system operating in a nonstationary environment with general time-varying arrival rates. Servers are cross-trained to help nonprimary customer classes during demand surges. However, such flexibility comes with various operational costs, such as a loss of efficiency and inconvenience in coordination. We characterize how to incorporate the future arrival information into the routing policy to balance the tradeoff between various costs and quantify the benefit of doing so. Based on transient fluid control analysis, we develop a two-stage index-based look-ahead policy that explicitly takes the overflow costs and future arrival rates into account. The policy has an interpretable structure, is easy to implement and is adaptive when the future arrival information is inaccurate. In the special case of the N-model, we prove that this policy is asymptotically optimal even in the presence of certain prediction errors in the demand forecast. We substantiate our theoretical analysis with extensive numerical experiments, showing that our policy achieves superior performance compared with other benchmark policies (i) in complicated parallel server systems and (ii) when the demand forecast is imperfect with various forms of prediction errors. Funding: This work was supported by the National Science Foundation Civil, Mechanical, and Manufacturing Innovation Grant 1944209. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0282 .