The Use of Simulation to Evaluate Optimisation-Generated Master Surgery Schedules

Abstract

During the COVID-19 pandemic, many elective surgeries had to be rescheduled as resources suchas beds and ventilators were reallocated, causing significant delays in patient care. To avoid such disruptions in the future effective resource management and planning approaches for elective surgery are essential. Optimisation is a commonly used method to enhance elective operating theatre scheduling, it is a technique used for mathematical modeling. It can integrate various criteria to maximise benefits and minimise costs within specified constraints. However, optimisation alone often falls short in addressing the complexities and required flexibility of operating theatre scheduling. This is where simulation can build upon these limitations. Simulation techniques can model system behaviour by replicating real-world processes, introduce uncertainty, and evaluate responses to different policies, helping to identify bottlenecks and improve system efficiency. Sequencing optimisation and simulation can test theoretically sound solutions under real-world uncertainties and complexities. This leads to the following research question:

“How can Discrete Event Simulation evaluate optimisation-generated Master Surgery Schedules for operating theatres?”

The research question focuses on a Master Surgery Schedule, which coordinates different surgical specialities, sharing OTs and pre- and post-surgery resources. While this approach increases resource utilisation, it also adds complexity by needing to accommodate the varying requirements of each speciality. The research aims to evaluate different Master Surgery Schedule using Discrete Event Simulation to contribute to the optimisation model.

Overall, the use of the Discrete Event Simulation model provided detailed insights into the
performance of various schedules. Testing these schedules under different types of uncertainty
demonstrated their robustness, as the behaviour remained consistent across scenarios. By
comparing the schedules side by side, the simulation model effectively evaluated their
effectiveness, ensuring the intended purposes were served and identifying areas for improvement.

The research specifically considers Discrete Event Simulation as this method can queue patients for different resources and have them move throughout the system based on decision rules. It is also a standard applied method for modelling healthcare systems. Both Discrete Event Simulation and optimisation are standard methods for improving OT scheduling. Even sequencing the methods has been proven to contribute to OT scheduling. However, applying this approach to a Master Surgery Schedule is new and introduces additional complexity related to the shared OTs and pre- and postsurgery resources.

To explore this research question, a case study was conducted at Sophia Children’s Hospital in
Rotterdam. Previous research developed the Master Surgery Schedule using an optimization
model, resulting in four different schedules. These schedules either balanced ward leveling and operating theatre utilization equally or prioritized ward leveling. They also varied in computational requirements, as the model updated the bed availability either every 15 minutes or every hour. This research categorizes 18 different surgical departments into 50 groups based on their surgery duration and length of stay, assigning time slots to these groups in the schedules.

This research uses these groupings to fit different distributions for the input variables of length of stay and surgery duration. Five different types of distributions were tested for each group, and the best-fitting distribution was assigned. Additionally, previous research provides a schedule for ward capacity and establishes decision rules for patient management. In collaboration with the hospital, the probability of Intensive Care assignment and the various decision rules were validated.

The sensitivity analysis revealed a slight overestimation of surgery duration compared to the test data, but this did not significantly impact outcomes. The model is more vulnerable to ward capacity and length of stay, which were then selected for scenario analysis. The schedule prioritising ward levelling and checking availability every 15 minutes outperformed others, effectively addressing ward unavailability, the primary bottleneck. However, increasing capacity improves the number of successful surgeries but also leads to more cancellations due to operating theatre unavailability and increased overtime occurrences. This highlighted a trade-off between operating theatre utilisation and other Key Performance Indicators.

The sensitivity analysis revealed a slight overestimation of surgery duration compared to the test data, but this did not significantly impact the overall outcomes. The model was found to be more sensitive to ward capacity and length of stay, which were then selected for scenario analysis. Among the different schedules, the one prioritizing ward leveling and checking bed availability every 15 minutes outperformed the others, effectively addressing ward unavailability, which was identified as the primary bottleneck. However, while increasing ward capacity improved the number of successful surgeries, it also resulted in more cancellations due to operating theatre unavailability and increased overtime occurrences. This finding highlighted a trade-off between operating theatre utilization and other Key Performance Indicators.

In line with the literature, the research reveals that striving for increased operating theatre
utilisation puts excessive pressure on other resources. Ward unavailability is identified as the main reason for surgery cancellations, indicating that wards require even greater focus. An increase in ward capacity had the best outcomes during the scenario analysis, showing that this is the biggest bottleneck in the system.

The simulation model identified new parameters for the optimisation model and highlighted
weaknesses in the system to be improved upon. Future research should explore ward capacity in greater detail and develop better methods for sharing resources across different operating theatres and wards to reduce the differences in utilisation. Additionally, further research could investigate other causes of surgery cancellations and refine the definitions of surgery groups