Creating resident shift schedules under multiple objectives by generating and evaluating the Pareto frontier

Creating shift schedules for medical residents is challenging, not only because of the large number of conflicting rules and requirements needed to ensure both adequate patient care and resident educational opportunities, but also because there is no one clear, well-defined single objective function to optimize. Instead, many factors should be taken into account when selecting the “best” schedule. In our practical experience, it is impossible for the scheduler (typically, a Chief Resident) to accurately determine weights that would allow these factors to be captured in a mathematical objective function that truly represented their preferences. We therefore propose to instead provide the Chief with a set of Pareto-dominant schedules from which to select. We present an integer programming-based approach embedded within a recursive algorithm to generate these schedules. We then present both computational results to assess the tractability of our approach and a case study, based on a real-world scheduling problem at the University of Michigan Pediatric Emergency Department, to study how a Chief Resident would evaluate the Pareto set.