Optimising OR planning

Optimising OR planning: Sequencing surgery groups while levelling bed occupancy

Vos, Kelly (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Discrete Mathematics and Optimization; Sophia Children’s Hospital)

van Essen, J.T. (mentor)
van Iersel, L.J.J. (graduation committee)
Staals, L.M. (graduation committee)
Keijzer, M. (graduation committee)

Delft University of Technology

Applied Mathematics

2023-03-13

This research is conducted in collaboration with the Sophia Children's Hospital (SCH). The hospital wants to provide their patients with more detailed information about when a patient is approximately scheduled to have a surgery. The first step is to create a model which optimises the operation room (OR) schedule and indicates when different kinds of surgeries are planned. This information, combined with the waiting list, provides insight in when a surgery of a specific patient is scheduled.

In a hospital, different departments work together to treat the patient as good and efficient as possible. If a patient needs a surgery, not only an OR is needed, but also a bed at a ward which matches the patient's needs. The goal of this thesis is to use the different resources of the hospital as efficiently as possible. This is done by not only optimising the utilisation of the OR, but at the same time levelling the bed occupancy of the different wards. The levelling of the bed occupancy is done by minimising the maximum number of used beds at each ward. Because, if we minimise the maximum, we force that the patients are spread out more evenly over the day.

For each specialty, the patients are divided into patient groups based on historical data using a constrained $k$-means clustering algorithm. For each patient group, information is gathered about the length of stay (LoS) and the surgery duration of patients in this patient group. Next to that, the number of patients in a patient group indicates how often a patient group needs to be scheduled at least.

The probability distribution of the surgery duration is taken into account when deciding at which day, at what time, and in which OR a surgery is planned. A patient group can only be scheduled during OR shifts assigned to the corresponding specialty. At the same time, the levelling of the bed occupancy is taken into account.

After some constraints are linearised, this model can be formulated as a mixed integer linear program (MILP). However, the model has a large number of variables. Therefore, column generation is used to split the model into smaller subproblems per specialty. Some of the pricing subproblems take a lot of time to optimise. For that reason, we set some time limits both on the runtime of the pricing subproblems and the runtime of the entire algorithm. Column generation does not guarantee an optimal solution of our MILP. However, the objective value of our MILP improves over time, when new columns are added to the set of available columns. This indicates that column generation can be used to optimise our model.

In this thesis, several versions of the model are presented. For example, the schedule is different if the bed occupancy is calculated every hour or of every fifteen minutes. Next to that, the model can either be more focussed on maximising the OR utilisation or on levelling the bed occupancy.

Optimisation
Optimisation in healthcare
Column Generation
OR planning

http://resolver.tudelft.nl/uuid:a808976d-31a5-40a1-bd14-e978f6e414ff

Student theses

master thesis

© 2023 Kelly Vos