Scheduling medical residents’ training at university hospitals

Medical residents need to successfully undertake a minimum number of surgical procedures across a variety of medical areas in order to complete their training. This paper addresses the problem of determining monthly training schedules for medical residents with the objective of minimizing the tardiness of their training. We develop a mixed integer programming (MIP) model which determines the number and type of surgical procedures a resident performs each month by assigning surgeries to residents subject to various constraints such as the limited availability of surgeries and the residents’ availability to perform surgical procedures. For small problem instances, the MIP model can be solved to near optimality using commercial solvers such as CPLEX. To solve larger instances, we propose a matheuristic combining Benders decomposition (BD) and ant colony optimization (ACO). The BD component of the matheuristic features a novel cut generation strategy which can be generally used to accelerate solving MIP models based on so-called step variables. We report on computational experiments showing that our novel cut generation strategy accelerates BD and our developed matheuristic is capable of finding good solutions quickly.