# A Review of the Scheduling Problem within Canadian Healthcare Centres
## 1 Introduction  
The scheduling problem in hospitals is a difficult problem to address, but an important one. Given the recent rise of COVID-19, this has been increasingly important as it has shown how limited resources are. In Canada, during the initial outbreak, many hospitals nationally were pushed to their breaking point with all elective surgeries and a large portion of visits being cancelled in attempts to alleviate the traffic. This could have, in part, been reduced with better utilization of their resources. Many outpatients were turned around at the door and staff were made to work long stressful hours. Additionally, many staff in Canadian hospitals are underwhelmed or disappointed with their schedules and are actively in need of a better solution. Surveys have shown that 24.5% of physicians are not satisfied with their careers due to the stress they are put under [1], operating rooms are only used at 68% of their potential on average [2], and at the Ottawa hospital residents report that the worst task they are assigned is creating schedules by hand [3]. These are just a few anecdotes, but they highlight the demand for better scheduling that exists within Canadian hospitals. With more efficient rostering, they could both allow more patients to access the care they need and alleviate some of the work that the staff needs to do. The focus is on Canadian papers in particular as Canada performs poorly on several important metrics. Canada is ranked ninth out of 11 when compared to other high-income countries [4]. In 2017, Canada had far fewer physicians overall compared to the international standard with 2.7 per capita compared to 3.5 [5]. Additionally, among Canadian physicians, over 5/6 ths meet the requirements for burnout [6]. They were also over three times more likely to show signs of depression [6]. It is known that when scheduling improves, so does both patient outcomes [7] and staff wellbeing [8]. By understanding how scheduling is done and exploring how to improve, healthcare in Canada can improve. This leads to the next problem that comes with scheduling: its complexity. Scheduling is an NP-Hard problem. The search space for creating a schedule grows exponentially so finding an efficient solving technique is a challenge. When creating a schedule thereare often dozens of constraints and an uncountable number of candidate solutions. With every new staff member, appointment, or rule, the time needed to find a solution increases exponentially. Furthermore, finding the optimal solution is not always possible due to time constraints of computing limits, so one often has to settle for a roster that is only satisfactory. This can mean either cutting the algorithm short or applying additional metaheuristic algorithms to improve solutions until they are acceptable. Many papers have attempted to develop strategies and software to address these problems, but given the large variety of use cases, this has led to a large variety of solutions. There are four main categories of hospital scheduling problems that are often looked at in Canada. The first of these categories is about how to schedule the staff. Hospitals need nurses, specialists, students, residents, etc., to be on the floor every day. The second type involves scheduling physicians to work in the emergency rooms. This is typically separated from general roster scheduling, as the addition of the emergency room adds additional considerations and it is typically more important due to the nature of the work. The third topic that is often reviewed is how to schedule operating rooms to be used. Operating rooms are one of the most important resources a hospital has, and therefore needs to be handled appropriately. Finally, the last category covers how to schedule outpatients and appointments. Given these distinctions, Section 4 will cover each of these scheduling topics in-depth and how they have impacted Canadian hospitals. Section 2 gives our methodology for selecting the papers.