# Bounding the Likelihood of Exceeding Ward Capacity in Stochastic Surgery Scheduling
## 3 Experimental Study
### General Surgery at Landspitali Hospital  
Landspitali Hospital is a national university hospital located in Reykjavik, Iceland. The hospital has approximately 650 ward beds and 15,000 surgeries performed annually by 11 surgical specialties. Only one of these specialties, General Surgery (GS), will be the focus of this study. The GS specialty performs upper and lower abdomen surgeries and consists of nine surgical operators. The specialty performs around 1200 elective surgeries annually, with up to 40% of the surgeries requiring ward admission.  
Landspitali Hospital uses block scheduling, where the MSS has been predetermined for the specialties and is repeated every five working days. The GS specialty is allocated to 13 blocks each week. The specialty then allocates these blocks to the operators in advance, each receiving at least one day of the week. The Friday blocks are shared between operators needing additional OR capacity. Each patient is assigned to an operator's waiting list and can be scheduled to one of the operator's blocks. There are two types of patients considered for the elective schedule: in- and out-patients. In-patients require a ward bed after their surgery to recover for one or more days, while out-patients leave the hospital the same day.  
In practice, patients are assigned to blocks by a human scheduler. Their selection is mainly dependent on their medical priority determined by the operator, their availability and readiness. At the hospital, two block lengths are available. On Mondays-Thursdays, the OR'a block length is 450 min, but it is 330 min on Friday. Due to the time limitation, patients must also be scheduled in such a way that the accumulated sum of their expected surgery times fits within the given block. However, going beyond the block capacity is possible, since two ORs are kept open longer for acute patients. As a result, the GS speciality utilises extended overtime. That is to say, it is preferable to have a small number of ORs that go into extended overtime rather than having a large number of ORs that go into regular overtime over the entire planning horizon. However, the time added to the extended block length is limited to 60 min.  
The GS specialty has limited access to downstream resources shared with other specialties. The scheduler takes these limitations into account by applying the following heuristic: each day, only one ICU patient can be admitted to the ICU, and in total, there are six staffed ward beds. Due to the limitations on the number of staffed ward beds, the scheduler uses the expected LOS (maximum of 7 days) for each surgery to determine the ward occupancy of each day. Using the expected values, however, has often resulted in cancellations. The ORs are utilized close to full capacity, but uncertainties in surgery duration and LOS in wards lead to last-minute cancellations, either due to overtime or ward overflow. The GS specialty wants to maintain a high level of throughput and reduce the number of last-minute cancellations. Today, it is common to plan patients up to two weeks in advance. However, the specialty would like to plan further ahead.