Linear approximations to improve lower bounds of a physician scheduling problem in emergency rooms

The physician assignment process consists of coverage of shifts and duties allocated to physicians in a planning period, taking into account work regulations, individual preferences, and organizational rules, which mostly conflict with each other. In this work, we propose a reformulated mixed-integer programming model based on the literature to tackle fairness in physician scheduling in Emergency Rooms (ERs). In particular, we propose two mixed-integer quadratic programming formulations that consider quadratic costs and two models with linear costs. Our approaches provide balanced schedules concerning target hours and weekends in terms of fairness. Our models also provide a high degree of demand coverage, providing decision-makers a significant advantage.