Multilocation, Dynamic Staff Planning for a Healthcare System: Methodology and Application

This paper presents the development, validation, and implementation of a data-driven optimization model designed to dynamically plan the assignment of anesthesiologists across multiple hospital locations within a large multi-specialty healthcare system. We formulate the problem as a multi-stage robust mixed-integer program incorporating on-call flexibility to address demand uncertainty. In the first stage, anesthesiologists are assigned to specific locations or an on-call pool several weeks before the day of surgery. In the second stage, on-call staff are deployed to particular locations based on demand forecasts received days before the surgeries. Finally, in the third stage, overtime and idle time are realized. To ensure practicality and real-world applicability, the model considers individual anesthesiologist location constraints and incorporates fairness considerations for on-call assignments. We exploit the problem's structure to reformulate the multi-stage robust optimization problem into a large-scale mixed-integer linear program. To solve this optimization problem efficiently, we propose a nested column and constraint generation method. Uncertainty in demand forecasts and workload is estimated based on historical data, with a calibration procedure that balances optimality and conservatism. The optimized dynamic staffing plan has been successfully implemented in the University of Pittsburgh Medical Center healthcare system, leading to estimated annual cost savings of 12\% compared to current practice, or about \$800,000 annually. We also provide managerial insights into the importance of improved forecasts, location flexibility, and the impact of fairness constraints. The proposed methodology is generalizable to other areas of healthcare staffing, such as nurse staffing, with similar workforce planning challenges.