Physician Scheduling in Emergency Rooms Michel Gendreau 1,2 , Jacques Ferland 1,2 Bernard Gendron 1,2 , Noureddine Hail 1 , Brigitte Jaumard 1,3 , Sophie Lapierre 1,4 , Gilles Pesant 1,4 , and Patrick Soriano 1,5 1 Interuniversity Centre for Research on Enterprise Networks, Logistics and Transportation (CIRRELT) Universit´ e de Montr´ eal, C.P. 6128, succ. Centre-ville, Montreal, Canada, H3C 3J7 michelg@crt.umontreal.ca 2 D´ epartement d’informatique et de recherche op´ erationnelle, Universit´ e de Montr´ eal 3 Concordia Institute for Information Systems Engineering, Concordia University 4 D´ epartement de math´ ematiques et g´ enie industriel ´ Ecole Polytechnique de Montr´ eal 5 Service d’enseignement des m´ ethodes quantitatives de gestion, HEC Montr´ eal Abstract. We discuss the problem of constructing physician schedules in emergency rooms. Starting from practical instances encountered in six different hospitals of the Montreal (Canada) area, we first we pro- pose generic forms for the constraints encountered in this context. We then review several possible solution techniques that can be applied to physician scheduling problems, namely tabu search, column generation, mathematical programming and constraint programming, and examine their suitability for application depending on the specifics of the situa- tion at hand. We conclude by discussing the problems encountered when trying to perform computational comparisons of solution techniques on the basis of implementations in different practical settings. 1 Introduction Constructing schedules (rosters) is not an easy task to accomplish in settings where work must be performed 24 hours per day and 7 days a week, such as in police and fire departements, or in emergency rooms of hospitals. The prob- lem that one is faced with is to generate “good schedules” that satisfy many complicated rules, including ergonomic rules as defined by Knaunth [20, 19]. As mentioned by Carter and Lapierre [11], ergonomic constraints are very impor- tant in order to manage the circadian rhythm of the staff and it is critical to take them into account when building schedules. In this paper, we focus on the problem of the scheduling of physicians in emergency rooms (ER) in health care institutions where work is continuous. It is known that ER are a very stressful place for physicians, but it is also great challenge for them to work in such a place. According to Lloyd et al. [23], 24.5% of physicians in Canadian ER are not satisfied with their jobs. Consequently, mak- ing a “good” schedule for physicians in ER is very important. A good schedule for a physician is a schedule that satisfies a large number of the requests he or E. K. Burke, H. Rudová (Eds.): PATAT 2006, pp. 2–14. ISBN 80-210-3726-1.