Managing Flexible Capacity in Service Systems with Worker Shortages

Problem definition: We study innovative capacity-planning strategies for service systems that encounter significant challenges in maintaining service quality because of worker shortages, a prevalent and growing issue across healthcare, retail, customer service, and other labor-intensive sectors. Methodology/results: Using a stylized queueing model representing a centralized service system, we propose a multistage staffing strategy utilizing capacities of various flexibility. Accounting for demand uncertainty and limited worker supply, our model prescribes dynamic staffing decisions, including long-term base staffing, short-term agency staffing, and the allocation of agency staffing in real time. We establish the convexity of the exact cost functions under a reasonable assumption of customer patience. To gain further insights, we characterize approximate solutions under stochastic fluid approximation. We then leverage these approximate solutions to quantify the benefits of flexible capacity in mitigating worker shortages, specifically by analyzing server utilization and cost reduction. A case study using hospital data validates the effectiveness of our staffing solutions; the annual cost reduction can reach at least half a million dollars by switching from independent agency staffing to pooled agency staffing if their unit staffing costs are comparable. Managerial implications: Our study demonstrates that incorporating flexible capacity alleviates heavy utilization of long-term capacity, preventing worker burnout in understaffed systems and ultimately improving the quality of service in the long run. In addition, employing flexible capacity effectively reduces system cost—a combination of staffing and delay costs that reflects the severity of shortages. In terms of cost reduction, a pooling strategy proves to be particularly advantageous when the demands of service units are volatile and countermonotonic. Interestingly, because pooling induces high server utilization (which likely further reduces congestion), a pooling strategy may recommend a higher total capacity than an independent staffing strategy, contrary to the common wisdom that pooling reduces resource requirements. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0271 .