# A Review of the Scheduling Problem within Canadian Healthcare Centres
## 4 Hospital Scheduling in Depth
### Operating Room Scheduling
#### 4.3.2 Papers
As of the writing of this paper, COVID-19 was still ongoing and putting strain on the hospital system and putting pressure on the number of available beds. This was one of the inciting forces in researching this problem. GORPS involves optimizing the act of scheduling patients to each day, members of resources to each timeslot, members of resources to patients, and creating a surgical scheduling block. To solve this problem they create a mixed-integer programming model using four different paradigms to compare and contrast how each performs. The four paradigms are sequence-based, immediate sequence-based, position-based, and time-based. A sequence-based model focuses on surgery pairs that can be assigned to a member. This version does not assume that the precedence between the pair is immediate. Essentially it attempts to come up with the most optimal ordered list of schedules. Immediate sequence-based scheduling does assume that the precedence is immediate. Position-based scheduling is where each patient is allotted one position in a list of resources, however, multiple resources can occupy the same position. This is the most common paradigm used in papers featured here and it was first introduced in this paper by [PERSON] and [PERSON] [19]. Time-based is the a growing paradigm that is more popular in more recent papers. It involves taking each time parameter (day, shift, time period) and discretizing them. After each surgery would be allotted a time slot. These four paradigms offer four different approaches to encoding the data and building the model. A fifth constraint programming model is introduced as well, while harder to solve for optimality, it is more than capable of returning a satisfactory solution. Another improvement that is made is assuming that overtime is a discrete variable as opposed to a continuous variable. This heavily punishes going over specific thresholds. Likewise to [PERSON] et al. [2], [PERSON] et al. [21] implement [PERSON]'s decomposition to reduce the scope of the problem and to explore other options, such as Branch and Check to compare decomposition methodologies. [PERSON] et al. [21] use data gathered from the General Surgery Department of the Toronto General Hospital (TGH). It spans July 2011 through June 2013 and contained 2711 surgeries. The best model was able to receive an optimality gap of 24.69% while the constraint program does considerably worse with an average optimality gap of 70.37%. Using logic-based Benders decomposition the average optimality gap was reduced to 2.71%. It was found that the constraint programming model was inefficient in comparison to linear programming models, even when computing subproblems. The paper concludes with insights into how TGH should react given this information. COVID-19 has resulted in a large backlog of cancelled surgeries due to the restrictions placed on elective visits. To account for these new patients, the models are rerun with additional instances of patients and this gives insight into how many additional patients the current resources can handle. It was concluded that the bottleneck was not the number of operating rooms but rather downstream resources such as ICU beds which prevented increases in patients. Investment into this area could dramatically increase revenue and throughput. Future work could be done to implement stochastic processes such as simulating patient arrivals or to further improve upon computational aspects of the models. [PERSON] et al. [36] look into the issues that are presented by appointment scheduling with heterogeneous service sequences. First, they assume that patients can be scheduled to do many different sequences. Some may show up for a checkup, while others may have surgery. The scheduling is done using a mathematical programming model. To incorporate the stochastic elements, they use discrete event simulation (DES) modelling. The simulation is a lognormal distribution that determines aspects such as the number of patients or open ORs.