An integer programming approach for the physician rostering problem

This paper presents an integer programming model and a matheuristic for the physician rostering problem. Constraints related to physician’s preferences, legal restrictions, hospital requirements and workload balance are investigated. Moreover, a comparison of physician and nurse rostering is analyzed to identify common constraints present in both problems. The lack of a mathematical model that could be applied in the studied problem motivated the development of a new formulation. Data and constraints of the proposed physician rostering problem were provided by Hospital de Clínicas de Porto Alegre (HCPA), Brazil. Due to the difficulty of solving large instances, a matheuristic which combines integer programming and heuristic techniques was proposed to approach the problem. Computational experiments were conducted employing commercial and open-source solvers. Results revealed that open-source solvers are a good alternative to solve small problems, while the proposed matheuristic generated near-optimal results within acceptable computation time employing larger instances.