Scheduling cardiac catheterization laboratories with Monte Carlo simulation

Abstract

The growing demand for cardiovascular treatments and the need to control the ever rising health care expenditures require efficient use of expensive resources, such as cardiac catheterization laboratories (cath labs). These in cardiac catheterization specialized operating rooms are labor and capital-intensive. Therefore, a high utilization is desired, although overtime should be prevented. However, this is complex in practice, because uncertainty in procedure duration and the number of patients makes it difficult to predict shift duration. At the moment, scheduling is mainly done by hand and the result strongly depends on the scheduler’s experience. Furthermore, little research is done on cath lab scheduling. Hence, this study aims to further define the cath lab scheduling process, identify the areas of improvement, and explore the usefulness of Monte Carlo simulation to support human schedulers. Schedulers of two Dutch hospitals, the Reinier de Graaf Gasthuis and the HagaZiekenhuis, are interviewed to map the scheduling process and identify the main difficulties. According to the schedulers, the main area of improvement is the estimation of procedure and shift duration, which currently is based on experience and rules of thumb. Based on the process in the HagaZiekenhuis, a Monte Carlo simulation is developed that computes the shift duration, utilization, and number of deferrals based on the blueprint schedule, the distributions of procedure duration and the emergency arrival rate. A first attempt to validate the model is done with input data from the VUmc as reported in another paper, as no historical data of the HagaZiekenhuis was available. The number of simulations required for convergence of the model was found to be at least 300. Next, the utilization, overtime, and undertime of the simulation were compared with these metrics from the VUmc. They were found to be close, even though the scheduling decisions are based on another hospital. To examine the sensitivity of the model, several scenarios are tested, namely, no emergency arrivals, a double amount of emergency arrivals, both halving and doubling the standard deviation of input distributions, adding extra patients to the inpatient waiting list to increase the demand, changing the threshold when patients are deferred and changing the type of input distribution from lognormal to normal. The effect of these scenarios is mainly as expected. Less variation in the output can be obtained by reducing the variance of the input distributions. Additionally, the type of input distribution seems to have limited effect on the output distribution. Furthermore, the effect of changing the deferral threshold, which is stochastic according to the interviews, seems limited. Moreover, no inexplicable behaviour was discovered by inspecting the realizations of the blue print schedule. Lastly, the data of the VUmc was applied to the blueprint of the HagaZiekenhuis, but inspection of the blueprint schedule revealed that the procedure duration in the VUmc data is longer than in the HagaZiekenhuis. This demonstrates that one cannot use the data and blueprint of different hospitals. An attempt was done to correct for this by scaling the distributions such that the mean corresponds to the scheduled duration. This led to more realistic results for some procedure types, although the standard procedure duration appears to not match the average duration for other types. The first results are promising, hence, a more in-depth validation of the model is recommended. The most promising application of this simulation seems the estimation of shift duration given a specific set of patients, integrated in the scheduling software.