Surgery Scheduling

Abstract

Scheduling surgeries in a hospital efficiently is a hard, but necessary task, because the Operating Rooms (ORs) contribute for about 40% of a hospitals total expenses. Therefore, we want to maximise the utilisation of the ORs. However, we want to prevent overtime, since there already is a lot of pressure on hospital employees. The overtime is not easily calculated, because of the stochastic nature of the surgery duration. In this thesis, we focus on maximising the utilisation of the ORs, without creating too much overtime. We model the scheduling of surgeries as integer linear programs (ILPs), which determine how many surgeries can be planned with the maximisation of the utilisation of the ORs as the objective. Different methods are used to include the overtime constraint and the resulting schedules are then compared and we take our conclusions. In our research, we use data provided by an academic hospital in the Netherlands, which provides spe-cialties, patient groups, a Master Surgery Schedule (MSS) and historical surgery durations. It also provides a minimum number of surgeries that have to be performed for each patient group. Preferably, we want to avoid overtime altogether. This however is not possible, due to the stochastic nature of the surgery duration. Instead we formulate an overtime constraint, by setting a probability that a surgery has to end within the opening hours. We call this, the overtime constraint. The premise of the first model is to create all possible combinations of surgeries which do not exceed the overtime constraint. In this model we create a variable which gives the distribution of the total surgery duration in a single OR on a single day. However, when adding multiple surgeries together we first need a distribution for the surgery duration. Unfortunately, we found that the surgery durations follow a log-normal distribution, which is supported by literature as well. The sum of log-normally distributed variables does not have a closed form, making it difficult to add the surgery durations together. To calculate the distribution of the total surgery duration, we use the Fenton-Wilkinson method. The second model discretises the opening hours of each OR into time blocks. We then define the probabil-ity that a surgery ends within a certain number of time blocks to incorporate the surgery duration. This way we can define a Mixed Integer Linear Program (MILP) without relying on any specific distribution. At first, we use historical data to create the probability that a surgery ends within a certain number of time blocks. However, to ensure we compare the different models fairly, we use the same log-normal distributions as the previous model and discretises them. We found that the Column Based Approach has a high utilisation and computes the columns and solves the ILP faster than the discrete model. Despite this, overtime can still occur with this approach. However, the number of times overtime occurs, remains well within acceptable limits. Additionally, the probability of no
overtime directly impacts utilisation, as intuitively expected...