Design of a mathematical model for staff planning in an emergency department

Abstract

The emergency department plays a fundamental role in hospitals and critically affects a hospital's overall efficiency. Inadequate staff planning in emergency departments generates high costs, overcrowding, and patient dissatisfaction due to long waiting times, possibly putting the patient's health and life at risk. This research designed two mixed integer linear programming mathematical models. The first determined the optimal number of physicians required per shift and weekday in an adult emergency department to minimize the deviation between available and required capacity. The results of the optimization model would reduce by 16.07 % the required medical office staff per week, from 56 physicians in the current situation to 47, reducing staffing costs without impacting waiting times. Moreover, the overall physician utilization would be 95.01 % compared to 77.79 % in the current situation, indicating an adequate distribution of physicians on each shift of each day according to patient demand. These results contribute to the problem of high medical staff costs and overcrowding without sacrificing timeliness and quality of care. In contrast, the second model that minimized the number of physicians considering capacity constraints would increase the staff by 7.14 % concerning the current situation. This research was based on a model presented in the literature, but the objective function included the deviation variables as unrestricted in sign and a constraint to ensure that they were positive. The first model designed is presented as a tool to support emergency department managers in the medium-term planning of medical staff, ensuring an optimal solution to this problem