Integrated staff scheduling at a medical emergency service: An optimisation approach

Abstract

Personnel scheduling is a difficult problem with many specific requirements that differ between industries or companies. This paper proposes an Integer Programming (IP) formulation for the staff scheduling problem encountered in practice at an Emergency Medical Services (EMS) system. Two types of heuristics (a diving heuristic and a VNDS heuristic) are implemented and extensively tested on a set of problem instances with different dimensions. Results show that the VNDS heuristic clearly outperforms both the diving heuristic and a state-of-the-art commercial IP solver. It is able to find good quality solutions for realistic problem instances in relatively short computation times. The characteristics that determine the relative difficulty of a problem instance are also investigated. Furthermore, the model is applied to a case study at the Portuguese National Institute for Medical Emergencies. For this purpose, the VNDS heuristic has been implemented in an expert system with an easy-to-use graphical user interface. A number of different schedules proposed by the system are compared with the schedule implemented in practice. This analysis shows that the VNDS heuristic is a significant improvement over the current manual scheduling procedure. Moreover, two what-if scenarios are described to show how the expert system can be used to assist managers in making decisions on contracting additional staff or providing training to workers.