An exact branch-and-price approach for the medical student scheduling problem

In this paper, we consider the medical student scheduling problem, which is a tactical scheduling problem assigning medical students to specific disciplines and hospitals in order to ensure an appropriate training over a one-year scheduling horizon. These internship positions are offered by local hospitals that specify minimum and maximum staffing requirements. To some extent, students can customise their own training program as they need to select a subset of the disciplines from an elective list and they are able to express their preferences related to these disciplines and the hospitals in which they would like to carry out their training program. The objective is to find a feasible student roster satisfying all educational and hospital requirements while optimising the student preferences and the equity between students. We propose an efficient branch-and-price algorithm to solve the problem under study. To that purpose, we include different dedicated mechanisms to accelerate the algorithm performance to find the exact solution in an acceptable time span. In this way, we propose a two-stage pricing procedure finding a diverse set of suitable columns to reduce the tailing-off effect in column generation. The pricing algorithm relies on dynamic programming and different pruning and symmetry breaking rules. In addition, the branch-and-price tree is constructed based on a mixed-shifting branching rule that executes different individual branching rules in a specific order. The created nodes in the branching tree are visited in the order determined by a novel right-first search strategy. We conducted different computational experiments to show the performance of the proposed branch-and-price and the implemented speed-up techniques and optimisation principles. We have benchmarked the branching and pricing methodology with other approaches and show the contribution of the different components in the algorithm. (C) 2021 Elsevier Ltd. All rights reserved.