# A Review of the Scheduling Problem within Canadian Healthcare Centres
## 4 Hospital Scheduling in Depth
### Outpatient Scheduling  
Outpatient scheduling is different from staff scheduling and is a prime example of type two schedules. It introduces the problem of updating a continuous schedule as opposed to creating a schedule from scratch each time. It is impossible to predict if, and when, patients will arrive because they are random in nature, meaning it is much harder to verify optimality. Additionally, one must consider factors such as rescheduling, cancellations, overtime, and downtime. Due to this stochasticity, simulations are typically used to stress test a model and determine its effectiveness. Some common considerations regarding this kind of roster are as follows:  
* Overtime should be capped at a maximum value [45]. * Each patient should be assigned a slot [45]. * Each timeslot should only be given one treatment [45]. * Overtime should be balanced between each nurse [45]. * Any patient can accept a timeslot [22]. * Multiple patients cannot occupy the same timeslot [22]. Papers  
The most common area of outpatient scheduling is in the field of oncology and cancer research [45; 47; 48; 50; 51]. It is the leading cause of death in Canada with over 233,900 cases in 2021 and 85,100 deaths [52]. It is estimated 40% of Canadians will be diagnosed within their life. Efficient scheduling of cancer outpatients could improve mortality and allow more patients to be seen. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Paper** & **Methodology** & **Data** \\ \hline [PERSON] and [PERSON] 2009 [46] & Neural Network, Simulation, Search & N/A \\ Heuristics, Tabu Search, Scatter Search & & \\ \hline [PERSON] and [PERSON] 2010 [22] & Multi-Agent Iterative Scheduling, MIP & N/A \\ \hline [PERSON] et al., 2014 [47] & MIP, Constraint Programming & Odette Cancer Centre in Toronto \\ \hline [PERSON] et al., 2015 [45] & Greedy Algorithm, Tabu Search & Regional Hospital at Trois-Rivières \\ \hline [PERSON] et al., 2016 [48] & Discrete-Event Simulation, Mixed Integer & British Columbia Cancer Agency Regional \\  & Linear Programming & Centre \\ \hline [PERSON] et al., 2020 [49] & Mixed Integer Linear Programming & Nephrology Division at The Ottawa Hospital \\ \hline [PERSON], [PERSON], and [PERSON] 2020 [50] & Discrete-Event Simulation, Mixed Integer & Centre Hospitalier Universitaire de Montreal \\  & Linear Programming & \\ \hline [PERSON] et al., 2020 [51] & Multi-Objective IP, Weighted Sum Method & Segal Cancer Centre in Montreal \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Outpatient Scheduling Papers. [PERSON] et al. [45] focus on the problem of appointment scheduling for chemotherapy. This type of schedule is unique as there are over 115 different types of treatments that can be done on a patient, each with its own duration, frequency, etc. To begin they build a mathematical programming model and gain their initial solution using a greedy algorithm. As patients come in they are added to the schedule wherever they fit. There are two ways they can do this: vertically and horizontally. Vertical scheduling is scheduling on a per-day basis and horizontal scheduling is scheduled on a per-period basis. To get a balanced initial solution a mixed treatment strategy is utilized which combines the two types of schedule additions. Following this, they attempt to solve the problem using tabu search. The tabu search will grade the solution based on the number of patients, the amount of overtime, and the nurse's workload. They use four neighbourhoods during this phase. The first neighbourhood they consider is the Fitting Lunch-break neighbourhood. This neighbourhood states that patients cannot start their treatment while a nurse is on their lunch break. The second neighbourhood is the Intra-Day neighbourhood. It reorders the treatments to fill in the gaps left by the previous neighbourhood. The third neighbourhood is the Consecutive Days Exchange neighbourhood. This one swaps the treatments of the consecutive days with the largest difference in patients seen. Finally, there is the Non-consecutive Days Exchange neighbourhood.