# A Review of the Scheduling Problem within Canadian Healthcare Centres
## 4 Hospital Scheduling in Depth
### Physician/Emergency Room Scheduling
#### 4.2.2 Papers
The second case study was replicated using a Constraint programming model by [PERSON], as cited by [PERSON], [PERSON], and [PERSON] [16], while it was able to create satisfactory solutions it was too intertwined with the problem as therefore was model inflexible. A third look at the physician scheduling problem comes from [PERSON] et al. [17] in the paper \"Physician Scheduling in Emergency Rooms\". They attempt to provide a general overview of the problem, defining constraints that should be considered and comparing and contrasting different models. The constraints are the main contribution to the paper. The incentive to address this problem comes from looking into practical cases at a series of Montreal-based Hospitals. The commonalities between them helped define the rules that should be considered when creating a roster. Almost a quarter of all physicians are dissatisfied with their job, and working to create better schedules is a place to start that is proven to be effective. The types of constraint distinctions are the same as stated above. To solve this schedule, they contrast and compare four different models: a mathematical programming model, a column generation model, a tabu search model, and a constraint programming model. For each of these models, they overview where they have been utilized and a general overview of how it works. [PERSON] et al. [1] bring a fourth look into physician scheduling with the paper \"Scheduling Emergency Room Physicians\". The same techniques and general constraints as covered prior are used to create their model. The data and ideas come from a survey of six major hospitals from Montreal. They also bring back the idea of cyclic schedules and create three different versions of the model: one acyclic, one cyclic with rotation, and one cyclic without rotation. To evaluate their approach to building models, they look into two different hospitals and compare their model results to those that are currently being used. The first hospital they observe is the Charles-Lemoyne Hospital (CLH). Within this hospital is the second busiest ER within Quebec. CLH currently uses a cyclic schedule without rotation over a planning period of 37 days, which results in a simple model. Few constraints are considered when creating the schedule, including vacation days. Despite this, most physicians like the schedule, as it is fair, predictable, and easy to remember. The main gripe people have expressed with it is that weekends are often divided between work shifts and off days. If a new schedule is to improve on the current methodology, it should keep what physicians like about the current schedule while fixing what they do not. Using tabu search, better schedules were found that managed to tick all the boxes. The best schedule was later implemented, and most physicians were pleased with the changes. The second hospital considered is Jewish General Hospital (JGH). JGH worked with acyclic schedules, and shifts were scheduled based on experience and teaching duty. This is a far more complicated system than the previous one. The drive to change the scheduling at this hospital stems from the amount of time it took to create. Around 40 h were devoted to preparing a schedule for three months. The physicians did like the schedules that were created, however. The authors were able to make a scheduler that could not only fulfill the requirements that were needed but could also consider physician's personal accounts. The other benefit that is offered to these two hospitals is the ability to fine-tune and change parameters at will. Allowing the model to be computerized permits them to make changes with a smaller amount of manpower and financial cost. [PERSON] et al. [31] decide to take physician scheduling a step further by implementing a productivity-driven schedule. Emergency rooms are extremely overcrowded in Canada, and those in Quebec are alleged to be the worst nationally. They define productivity with two metrics: the number of patients seen every hour, and a relative time unit.