# A Review of the Scheduling Problem within Canadian Healthcare Centres
## 4 Hospital Scheduling in Depth
### General Staffing/Nurse Staffing
#### 4.1.2 Papers  
[PERSON] and [PERSON] [19] dedicate their paper \"Cyclic nurse scheduling\" to creating a cyclic schedule for nurses. Nurses need to be scheduled around the clock and in a consistent manner so they are the perfect candidate to try cyclic scheduling. To demonstrate the effectiveness in search space reduction they go through the process of how the schedule is encoded. We will go over it here, as this is the way most schedules approach it. A schedule is defined as a string of binary characters representing the timeslot that a nurse would work. A '1' would represent a shift, while a '0' is the lack of one. In the case of this paper, there are 7, one for every day of the week. Other papers may go into the finer grain as they want to designate shifts at specific times. After, they then define the constraints that the schedule must obey, as seen above. This is known as the position-based approach. Working under these constraints acyclically brings the total possible solutions down to 22 candidates. The rules for a cyclic schedule are then introduced, which further reduces the solution pool to six possible solutions. It is not specified but they use cyclic schedules \begin{table}
\begin{tabular}{l l l} \hline \hline
**Paper** & **Methodology** & **Data** \\ \hline [PERSON] and [PERSON] 1987 [19] & Cyclic Integer programming & N/A \\ \hline [PERSON] et al., 1998 [20] & Generalized linear programming, Column Generation & Royal Victoria Hospital of Montreal \\ \hline [PERSON], [PERSON], and [PERSON] 2003 [13] & Constraint programming, Heuristics Search & Montreal-based hospitals \\ \hline White and White 2003 [3] & Tabu Search & Ottawa Hospital \\ \hline [PERSON] et al., 2007 [18] & Tabu search, Great Deluge, IDWalk & Ottawa Hospital \\ \hline [PERSON], [PERSON] 2015 [27] & Excel Based Heuristic & Notre-Dame and Sainte-Justine \\ \hline [PERSON] et al., 2019 [15] & Linear Programming & Ottawa Hospital \\ \hline [PERSON], [PERSON], and [PERSON] 2020 [28] & Linear Programming, Column Generation & N/A \\ \hline [PERSON] et al. [29] & MILP, Simulation & Vancouver Coastal Health \\ \hline \hline \end{tabular}
\end{table} 
Table 1: General Staffing/Nurse Staffing Papers. with rotation, meaning schedules can alternate but will have to repeat eventually. Building a cyclic schedule comes with some benefits. Firstly, the approach is very fast and very small. The total implementation was done on a 64 K 8-bit computer. Another benefit to cyclic scheduling is it is inherently repeating. This means that the schedule only needs to be solved one time as opposed to every period. In practice, constraints will change and schedules will have to be remade but this minimizes the creations. Finally, this approach is flexible to the constraints. Constraints can be added and removed at will and the model will still perform. This paper does not specifically test their model on any real-world data. For an example of a broader scope nurse scheduling model, we can look at \"A Constraint Programming Application to Staff Scheduling in Health Care\" by [PERSON], [PERSON], and [PERSON] [13]. In their paper, they have two different goals in mind. The first is to create software called Hibiscus which can be used to create rosters for staff scheduling problems in a flexible manner. The second is to create a modular architecture that allows heuristic searches to be implemented into the model. Hibiscus is designed to be generic so that it can be utilized in many different scenarios without having to redesign it from the ground up. To begin addressing this goal they define the main rule divisions: demand, availability, distribution, and ergonomics. Doing so not only allows Hibiscus to be able to talk about classes of constraints but it makes them more straightforward to implement. These implementations allow them to implement a large variety of constraints such that the software is flexible enough to be adopted into other hospitals. In an attempt to improve their model and make it stand out, they also introduce search heuristics to it.