Capacity Allocation and Scheduling in Two-Stage Service Systems with Multiclass Customers

Problem definition: This paper considers a tandem queueing system in which stage 1 has one station serving multiple classes of arriving customers with different service requirements and related delay costs, and stage 2 has multiple parallel stations, with each station providing one type of service. Each station has many statistically identical servers. The objective is to design a joint capacity allocation between stages/stations and scheduling rule of different classes of customers to minimize the system’s long-run average cost. Methodology/results: Using fluid approximation, we convert the stochastic problem into a fluid optimization problem and develop a solution procedure. Based on the solution to the fluid optimization problem, we propose a simple and easy-to-implement capacity allocation and scheduling policy and establish its asymptotic optimality for the stochastic system. The policy has an explicit index-based scheduling rule that is independent of the arrival rates, and resource allocation is determined by the priority orders established between the classes and stations. We conduct numerical experiments to validate the accuracy of the fluid approximation and demonstrate the effectiveness of our proposed policy. Managerial implications: Tandem queueing systems are ubiquitous. Our results provide useful guidelines for the allocation of limited resources and the scheduling of customer service in those systems. Our proposed policy can improve the system’s operational efficiency and customers’ service quality. Funding: Z. Zhong’s research is partially supported by the Fundamental Research Funds for the Central Universities [Grant 2023ZYGXZR074] and the Hunan Provincial Natural Science Foundation of China [Grant 2022JJ40109]. P. Cao’s research is partially supported by the National Natural Science Foundation of China [Grant 72122019]. J. Huang’s research is partially supported by the Hong Kong Research Grants Council General Research Fund [CUHK-14501621] and the National Natural Science Foundation of China [Grant 72222023]. S. X. Zhou’s research is partially supported by the Hong Kong Research Grants Council General Research Fund [CUHK-14500921], the National Natural Science Foundation of China [Grant 72394395], and the Asian Institute of Supply Chains and Logistics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0266 .