Customer Scheduling in Large Service Systems Under Model Uncertainty
Shiwei Chai, Xu Sun, Hossein Abouee-Mehrizi
Operations Research · 2025 · Volume 73 · Issue 2
Abstract
Scheduling in the context of many-server queues has received considerable attention. When there are multiple customer classes and many servers, it is common to make simplifying assumptions that result in a “low-fidelity” model, potentially leading to model misspecification. However, empirical evidence suggests that these assumptions may not accurately reflect real-world scenarios. Although relaxing these assumptions can yield a more accurate “high-fidelity” model, it often becomes complex and challenging, if not impossible, to solve. In this paper, we introduce a novel approach for decision makers to generate high-quality scheduling policies for large service systems based on a simple and tractable low-fidelity model instead of its complex and intractable high-fidelity counterpart. At the core of our approach is a robust control formulation, wherein optimization is conducted against an imaginary adversary. This adversary optimally exploits the potential weaknesses of a scheduling rule within prescribed limits defined by an uncertainty set by dynamically perturbing the low-fidelity model. This process assists decision-makers in assessing the vulnerability of a given scheduling policy to model errors stemming from the low-fidelity model. Moreover, our proposed robust control framework is complemented by practical data-driven schemes for uncertainty set selection. Extensive numerical experiments, including a case study based on a U.S. call center data set, substantiate the effectiveness of our framework by revealing scheduling policies that can significantly reduce the system’s costs in comparison with established benchmarks in the literature. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0144 .
Keywords
Stochastic Models, many-server queues, customer scheduling, abandonment, diffusion analysis, differential games
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