# A Review of the Scheduling Problem within Canadian Healthcare Centres
## 4 Hospital Scheduling in Depth
### Operating Room Scheduling
#### 4.3.2 Papers
This input is then sent to a bed utilization simulator (BUS) and the output is evaluated. The input is then updated with the output until a final surgical block schedule is generated. The framework consists of two models: an SSO to create the schedule, and a BUS is used to evaluate the schedule that was created. Now that schedules contain more stochastic elements, evaluating them goes beyond just satisfying constraints, and simulations must be run to determine their effectiveness. Starting with the BUS, which predicts ward bed's daily demand given an uncapacitated system, planned patients are predicted to arrive based on historical data and are then classified into patient types. Unplanned patients are generated using a Poisson distribution. These patients are then sampled to create ward occupancy patterns. The schedule is evaluated using the metric \"bed-days over capacity\", which is a measure of the number of extra beds and allows an estimate of patient off-servicing or surgery cancellation. The SSO used data from the BUS as well as surgical guidelines to create a schedule that optimizes bed occupancy. The SSO contained two models: a base model which assigns surgical blocks, and a slate model, which in addition to assigning surgical models also determines patient type mix within a given block. Both models are mixed-integer programming models. To fully evaluate this framework, a case study was done on the Royal Jubilee Hospital (RJH) in Victoria BC. This hospital is the main hospital for over 350 thousand residents, has 16 operating rooms, and 42 inpatient beds. Using both the BUS and the SSO led to a \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scenario** & **Description** & **Results** \\ \hline Present State Analysis & Evaluates model’s accuracy and current status & Returned the maximum number of beds utilized. \\ \hline Resource Optimization & Identifies schedules with a smaller number of beds and lower bed utilization fluctuations & When optimizing for bed usage, the model was able to require 39 fewer ward beds and a similar number of special care unit (SCU) beds. \\ \hline Waitlist Management & Determines how many resources are required to stabilize waitlists & When optimizing for waitlists the bed usage still decreased, this time by about four beds. \\ \hline System-Wide Analysis & Studies benefits of hospitals that collaborate & When using collaborative methods between hospitals, further bed reduction was possible. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Outpatient Scheduling Papers. 16% reduction in bed days over capacity. This means 13 cancellations or improper wards could have been avoided. When using the slate mode, an increase of 15 surgical cases was reported. This left to bed-days over capacity being reduced by 9% and surgical volume increasing by 5%. The model was able to produce this result in about 10 min, however, if optimality was desired it would take over six hours. The difference between the suitable solution and optimality was within 1%. [PERSON] et al. [43] do not work with a specific hospital but do review others that work with Canadian hospitals as well as justify their work with Canadian statistics. They look to solve the stochastic distributed delivery room problem. They first motivate their work with the statistic that 30% of patients who need hip replacements and other similar surgeries wait longer than the recommended wait time in Canada. This obviously can lead to detrimental outcomes on the patient as well as the staff. By producing better schedules they aim to improve this area of healthcare and allow better access to vital surgeries. They model their program as a 2 SIP (2-stage stochastic integer program) problem. As the problem is stochastic they first generate random scenarios to represent the length of each surgery. They solve the problem approximately based on each random vector and find an expected cancellation cost by averaging the results. With this information they are able to begin solving the problem more optimally with decomposition methods.