A robust framework for task-related resident scheduling

We consider the training phase of physicians after finishing medical school. They specialize in a common field like ophthalmology or anesthesiology and are called residents. Technological progress in health care leads to increasing complexity in the requirements of physician training. As a consequence, those programs are often not only time-related but also task-related. Task-related means that residents should perform a given number of different interventions in their program. Typically, a resident will follow a rotation across different clinical departments, where the number of performed interventions per period may be estimated. Predicting the exact number of interventions is usually not possible. Accordingly, a resident might not be able to perform all of the required interventions during the planned rotation, resulting in an extension of the program. In this paper, a new model is presented that calculates the number of residents a hospital can reliably train on a strategic level. Our model also provides the corresponding training schedule. It considers minimum requirements of both time-related stays in specific departments as well as task-related interventions that have to be performed. The robustness of the model can be set by management to handle uncertainties in interventions. A Dantzig–Wolfe decomposition is used to accelerate the solution process and a new pattern generation approach that can construct multiple patterns out of one solution is developed. The termination of the column generation algorithm is accelerated significantly by this method. The model is evaluated using real-world data from a resident program for anesthesiology in a German university hospital. The results demonstrate that near-optimal solutions with an average optimality gap of below five percent can be achieved within computation times of few minutes.