Productivity-driven physician scheduling in emergency departments

The objective of this study is two-fold: to propose an alternative approach for computing the productivity of physicians in emergency departments (EDs); and, to allocate productivity-driven schedules to ED physicians so as to align physician productivity with demand (patient arrivals), without decreasing fairness between physicians, in order to improve patient wait times. Historical data between 2008 and 2017 from the Sacre-Coeur Montreal Hospital ED is analysed and used to predict the demand and to estimate the productivity of each physician. These estimates are incorporated into a mathematical programming model that identifies feasible schedules to physicians that minimise the difference between patients' demand and physicians' productivity, along with the violation of physicians' preferences and fairness in the distribution of shifts. Results on real-world-based data show that when physician productivity is included in the allocation of schedules, demand under-covering is reduced by 10.85% and the fairness between physicians is maintained. However, physicians' preferences (e.g., sum of the differences between the number of wanted shifts and the number of allocated shifts) deteriorates by 7.61%. By incorporating the productivity of physicians in the scheduling process, we see a reduction in EDs overcrowding and an improvement in the overall quality of health-care services.