Operating room staffing and scheduling

Problem definition: We consider two problems faced by an operating room (OR) manager: (1) how many baseline (core) staff to hire for OR suites, and (2) how to schedule surgery requests that arrive one by one. The OR manager has access to historical case count and case length data, and needs to balance the fixed cost of baseline staff and variable cost of overtime, while satisfying surgeons’ preferences. Academic/practical relevance: ORs are costly to operate and generate about 70% of hospitals’ revenues from surgical operations and subsequent hospitalizations. Because hospitals are increasingly under pressure to reduce costs, it is important to make staffing and scheduling decisions in an optimal manner. Also, hospitals need to leverage data when developing algorithmic solutions, and model tradeoffs between staffing costs and surgeons’ preferences. We present a methodology for doing so, and test it on real data from a hospital. Methodology: We propose a new criterion called the robust competitive ratio for designing online algorithms. Using this criterion and a robust optimization approach to model the uncertainty in case mix and case lengths, we develop tractable optimization formulations to solve the staffing and scheduling problems. Results: For the staffing problem, we show that algorithms belonging to the class of interval classification algorithms achieve the best robust competitive ratio, and develop a tractable approach for calculating the optimal parameters of our proposed algorithm. For the scheduling phase, which occurs one or two days before each surgery day, we demonstrate how a robust optimization framework may be used to find implementable schedules while taking into account surgeons’ preferences such as back-to-back and same-OR scheduling of cases. We also perform numerical experiments with real and synthetic data, which show that our approach can significantly reduce total staffing cost. Managerial implications: We present algorithms that are easy to implement and tractable. These algorithms also allow the OR manager to specify the size of the uncertainty set and to control overtime costs while meeting surgeons’ preferences.