Improving physician schedules by leveraging equalization: Cases from hospitals in U.S

In this paper, we consider physician scheduling problems originating from a medical staff scheduling service provider based in the United States. Creating a physician schedule is a complex task. It must balance several goals, including adequately staffing required assignments to ensure quality patient care; adhering to rules that vary by hospital and medical specialty, and helping physicians to maintain work/life balance. We study various types of physician and hospital requirements with different priorities, focusing on achieving an equal distribution of the workload among physicians to produce a schedule that they perceive as fair, while all other group requirements are met. We observe that as the number of such equalization constraints increases, the physician scheduling optimization problem becomes more complex and it requires a longer time to find an optimal schedule. We begin by constructing mathematical models to formulate the physician scheduling problem requirements, and then for the relaxation of the problem that includes equalization constraints we derive a new class of valid inequalities, along with a polynomial separation algorithm for them. A branch-and-cut algorithm using these valid inequalities notably improves the quality of the schedules with respect to the soft constraints. We discuss in detail an example problem from a hospitalist department and present improvements to other schedules representing different specialties and hospitals.