# A Review of the Scheduling Problem within Canadian Healthcare Centres
## 4 Hospital Scheduling in Depth
### Operating Room Scheduling
#### 4.3.2 Papers  
A first look at scheduling operating rooms comes from \"Surgical block scheduling in a system of hospitals: an application to resource and waitlist management in a British \begin{table}
\begin{tabular}{c c c} \hline \hline
**Paper** & **Methodology** & **Data** \\ \hline [PERSON], [PERSON], and [PERSON] 2007 [34] & Mixed Integer Programming & Fraser Health Authority \\ \hline [PERSON] et al., 2011 [33] & Mixed Integer Programming, Monte Carlo & Royal Jubilee Hospital \\ Simulation & & \\ \hline [PERSON] et al., 2013 [26] & Discrete Event Simulation & Toronto General Hospital \\ \hline [PERSON] et al., 2013 [35] & Simulation Based Tabu Search, IP, BP & A Major Canadian hospital \\ \hline [PERSON] et al., 2015 [36] & Multi-Agent Tabu Search, Mathematical & A Major Canadian hospital \\  & Programming, Simulation & \\ \hline [PERSON] et al., 2016 [37] & Mixed Integer Programming, Discrete Event & University Health Network \\ Simulation & & \\ \hline [PERSON] et al., 2017 [2] & MIP, Bender’s Decomposition & University Health Network \\ \hline [PERSON] et al., 2017 [38] & MIP, Bender’s Decomposition & Toronto General Hospital, Toronto Western \\  & & Hospital, and Princess Margaret Cancer Centre \\ \hline Diamant, Milner, and Queenshy 2018 [39] & MIP, Column Generation, Lagrangian & Bariatric surgery Department in Toronto \\  & Constraints, Integrality & Western Hospital \\ \hline Rozario and Rozario 2020 [25] & Machine Learning & Oakville Trafalgar Memorial Hospital \\ \hline [PERSON] et al., 2020 [40] & Time Series Analysis, Statistical Analysis & Ontario based administrative data sources \\ \hline [PERSON] et al., 2020 [41] & Mixed Integer Linear Programming & Hospital in Quebec City \\ \hline [PERSON] et al., 2020 [42] & MIP, Bender’s Decomposition & University Health Network \\ \hline [PERSON] et al., 2021 [21] & Mixed Integer Programming, Benders & Toronto General Hospital \\  & Decomposition, Constraint Programming & \\ \hline [PERSON] et al. [43] & Mixed Integer Programming, Benders & N/A \\  & Decomposition & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Operating Room Scheduling. Columbia health authority\" by [PERSON], [PERSON], and [PERSON] [34]. Operating room scheduling differs from previous scheduling methods, as there are more variables to consider. Different specialties require different setups in the operating room, so they need to be scheduled differently. Factors such as wait time, capacity, and priority now need to be considered. In tackling this problem, [PERSON], [PERSON], and [PERSON] [34] define three stages of scheduling for this purpose. The first stage determines the amount of time each specialty should be allotted. The second stage divides the OR specialties up on a per-day basis, creating the schedule itself. This process is called the surgical block scheduler. The third stage schedules the individual patients. This paper focuses on how to construct the second stage. The first stage is assumed to be completed, and so creates a list of constraints that need to be followed. The schedule, created for the Frasier Health Authority, must follow the constraints given and must also be cyclic: able to be applied every week. The model created was a mixed-integer programming model and was solved for optimality the majority of the time. Data was analyzed from eight hospitals, with each one covering 4000 to 11,000 cases and from 3500 operating minutes to 15,000 operating minutes. From here, four main scenarios were analyzed and are summarised in Table 5.  
Overall, by focusing on optimizing the surgical block scheduler, it was possible to increase the throughput of patients while decreasing resource utilization. On average the model was able to reduce the number of ward beds by an average of 4.85 and the number of special care unit (SCU) beds by 0.05. [PERSON] et al. [33] offer a second look at creating a surgical block scheduler. They propose the following surgical scheduling framework: A surgical schedule optimizer (SSO) and scheduling guidelines are the input into the framework.