Physician scheduling in case managers style emergency departments: machine learning-aided solution approaches

Emergency department (ED) crowding has become a common phenomenon worldwide. A number of interventions have been proposed to improve operations in EDs, such as scheduling physicians to manage varying patient demands. Motivated by a collaboration with a large ED, we study physician scheduling in the ED. The ED is modeled as a time-varying case managers system where the number of patients simultaneously assigned to a single physician is limited by maximum caseloads. To match real-life scenarios, we consider time-varying patient arrivals, temporary ED overloading, and patient-physician assignments. We first analyze patient flow and service procedures using real data to capture the features of the ED. Next, a mathematical model of physician scheduling is constructed. To effectively solve this complex problem, two machine learning-based solution approaches are designed. The first approach integrates an extreme gradient boosting model with Gurobi. The second involves a variable neighborhood search algorithm, in which a long short-term memory network is incorporated to evaluate the solution to the problem. Numerical experiments indicate that the proposed approaches can yield high-quality solutions within reasonable time frames. The physician schedules generated by the second approach outperform those generated by the first approach and are also superior to the actual schedules used by our partner ED. For the data from the stable period, our solutions reduce the average patient waiting time and total physician working time by 10.32 % and 14.79 %, respectively, compared to the actual ED schedules. During the COVID-19 outbreak, these two metrics are respectively reduced by 8.06 % and 12.9 %.