Equity-promoting integer programming approaches for medical resident rotation scheduling

Motivated by our collaboration with a residency program at an academic health system, we propose new integer programming (IP) approaches for the resident-to-rotation assignment problem (RRAP). Given sets of residents, resident classes, and departments, as well as a block structure for each class, staffing needs, rotation requirements for each class, program rules, and resident vacation requests, the RRAP involves finding a feasible year-long rotation schedule that specifies resident assignments to rotations and vacation times. We first present an IP formulation for the RRAP, which mimics the manual method for generating rotation schedules in practice and can be easily implemented and efficiently solved using off-the-shelf optimization software. However, it can lead to disparities in satisfying vacation requests among residents. To mitigate such disparities, we derive an equity-promoting counterpart that finds an optimal rotation schedule, maximizing the number of satisfied vacation requests while minimizing a measure of disparity in satisfying these requests. Then, we propose a computationally efficient Pareto Search Algorithm capable of finding the complete set of Pareto optimal solutions to the equity-promoting IP within a time that is suitable for practical implementation. Additionally, we present a user-friendly tool that implements the proposed models to automate the generation of the rotation schedule. Finally, we construct diverse RRAP instances based on data from our collaborator and conduct extensive experiments to illustrate the potential practical benefits of our proposed approaches. Our results demonstrate the computational efficiency and implementability of our approaches and underscore their potential to enhance fairness in resident rotation scheduling.