Customer Scheduling in Large Service Systems Under Model Uncertainty

Scheduling in the context of many-server queues has received a lot of attention. When there are many servers and multiple customer classes, it is common practice to make simplifying assumptions, resulting in a ``low-fidelity" model, hence potential model misspecification. Real-world data suggests those assumptions may be far-fetched. Relaxing those assumptions may result in a high-fidelity model, but the model is likely to be complex and difficult (if not impossible) to solve. In this paper, we set forth a new approach for the decision maker to generate high-quality scheduling policies for large service systems such as call centers by relying on a simple and tractable low-fidelity model as opposed to its otherwise complex and intractable high-fidelity counterpart. At the core of this approach is a robust formulation in which the decision maker optimizes against an imaginary adversary. The adversary optimally exploits potential weaknesses in a scheduling rule by perturbing the low-fidelity model in a dynamic yet time-consistent fashion, assisting the decision maker in exploring the robustness of a candidate policy against possible model misspecification. Then, with a set of scheduling policies (generated with different robustness levels), a simulation can be set up to evaluate the performance of these policies and identify the best scheduling policy. We demonstrate through a numerical study based on a data set calibrated from a US call center that our approach allows us to identify scheduling policies that can achieve 10\% to 20\% cost savings compared to the established benchmark in the literature