A flexible integer linear programming formulation for scheduling clinician on-call service in hospitals

Scheduling of personnel in a hospital environment is vital to improving the service provided to patients and balancing the workload assigned to clinicians. Many approaches have been tried and successfully applied to generate efficient schedules in such settings. However, due to the computational complexity of the scheduling problem in general, most approaches resort to heuristics to find a non-optimal solution in a reasonable amount of time. We designed an integer linear programming formulation to find an optimal schedule in a clinical division of a hospital. Our formulation mitigates issues related to computational complexity by minimizing the set of constraints, yet retains sufficient flexibility so that it can be adapted to a variety of clinical divisions. We then conducted a case study for our approach using data from the Infectious Diseases division at St. Michael's Hospital in Toronto, Canada. We analyzed and compared the results of our approach to manually-created schedules at the hospital, and found improved adherence to departmental constraints and clinician preferences. We used simulated data to examine the sensitivity of the runtime of our linear program for various parameters and observed reassuring results, signifying the practicality and generalizability of our approach in different real-world scenarios.