# A Review of the Scheduling Problem within Canadian Healthcare Centres
## 5 Overview  
Most papers can be broken down into three components. The construction of the mathematical model, the construction of a solving algorithm, and a results section to verify the efficacy of the solver.  
When it comes to constructing a mathematical model, physician scheduling goes the most in-depth with nurses scheduling a close second. They have the most unique constraints and explore additional parameters such as nurse fairness and relative priority between different staff members. Outpatient and OR room scheduling explore far fewer constraints, leading to less variation between each model. Nurse and physician scheduling solvers are also more likely to be modular and generic, furthering the likelihood of compatibility within various hospitals. Both physician and operating room scheduling had instances of online and static scheduling, while nurse scheduling was solely static and outpatient was solely dynamic. With combinations missing, future work may be done. Figure 3 shows the choices made.  
The choice of model also helps determine which direction improvements may be done. With static instances, the research tends to explore improving the solvers for the models. Dynamic instances have more choices, often creating simulation models or constructing algorithms to predict probability distributions.  
A pattern worth noting is that exact methods have completely dominated the market in recent years. From 2016 on-wards no paper focuses on a metaheuristic, opting instead for integer linear programming with column generation or bender's decomposition. This method can be aborted early to get approximate solutions. This may be in part to long schedule creation periods and improvements in linear programming, however, with different requirements across the domain it is difficult to give exact reasoning. Of those that did include both exact and methods such as [PERSON] et al. (1977) [PERSON], [PERSON] and [PERSON] (2016), comparison and sensitivity analysis were minimal. Figure 4 shows some choices that may be made when choosing between which solving algorithm to utilize. Within the papers that do explore heuristics, the selection of heuristics chosen is very limited. Three major heuristics in Tabu search, local search, and genetic algorithms are chosen. Further exploration into additional heuristics may be warranted.  
While results have been nearly universally positive, direct comparison between different studies is difficult. Each paper provides a different problem to solve and few papers offer statistical analysis or comparison between different models. This results in a situation where improvement as a field is hard to quantify. Better evaluation within all domains would help. Comparisons between different solving methodologies or comparisons of schedules over significant periods would serve to better prove which methods are effec  
Figure 4: A flowchart of decisions to be made when choosing and implementing algorithms.  
Figure 3: A flowchart of decisions to be made when choosing the problem domain.  
tive. Figure 5 contains ways to evaluate your model and solver to better represent its effectiveness.  
By improving these three aspects of scheduling better timetables will be created.