A flexible discrete optimization approach to the physician scheduling problem

Personnel scheduling deals with the attribution of a number of duty shifts to a number of workers respecting several types of requirements. In this work, the problem of scheduling physicians in health care departments is studied. This problem is NP-hard, and we propose a flexible Mixed Integer Linear Programming formulation that allows easy modifications for representing different situations and scenarios. This formulation can be solved to optimality by a standard Branch-and-Cut procedure even for very long planning horizons. A real-world case study is considered. A comparison of the solutions obtained by the proposed approach with the solutions currently adopted in the considered structure is presented. Results are very encouraging both from the schedule quality (e.g., workload balancing) and from the computational point of view.