Actividad específica de los cantones de la Provincia de Chimborazo

This section describes the data we use for our simulation model. First, we discuss the ORs, session roster, specialties and specialists in Section 4.1.1. Section 4.1.2 explains the arrival of elective and emergency patients, and how we determine the surgery durations per patient. We conclude this section with an explanation on how we model the late (and early) starts of the OR sessions and the changeovers.

4.1.1.

ORs, session roster, specialties and specialists

HOH has five inpatient ORs and one outpatient OR. We assume that inpatients and emergency patients are only operated in the inpatient ORs, and outpatients are only operated in the outpatient OR. We use the session roster of January 2016 until June 2017 for the validation phase. Since we use data from the same period for the data analysis in Chapter 2, we make a fair comparison between the simulation model and realization. We use the roster of 2018 for the experiments, to obtain relevant results for current practice.

Table 4.1shows the specialties and number of specialists per specialty we simulate. In reality, there is one general surgeon who also performs Urology surgeries. For simplicity reasons, we choose to limit the type of surgeries to General Surgery for this specialist. Furthermore, simulating two cardiologists causes an overload for one of the cardiologists, i.e., the number of sessions is not sufficient to schedule all arriving patient. Therefore, we choose to simulate one cardiologist for all Cardiology sessions. This way the sessions of Cardiology are evenly loaded.

Table 4.1: Number of specialists per specialty

Specialties Number of specialists General Surgery 6 Ophthalmology 3 Gynecology 5 Orthopedics 4 Plastic Surgery 2 ENT 2 Urology 2 Neurosurgery 1 Pain treatment 1 Cardiology 1

4.1.2.

Patient arrival and surgery duration

Elective patients arrive according to a Poisson distribution with λ=0.822 per hour. Emergency patients arrive according to a Poisson distribution with λ=0.225 per hour on average. However, the number of emergency arrivals per hour varies. Therefore, we include a time dependent arrival rate per hour based on historical data. Figure 4.2 shows the emergency arrival pattern of the simulation model and the realization. Not all emergency surgeries are linked to a moment that the decision is made that the patient should undergo surgery, for this reason we give the number of arriving emergency patients per hour as percentage of the total amount of emergency patients and use this percentage to determine the time dependent arrival rate.

43 Figure 4.2: Arrival of emergency patients per hour in percentage

We use probabilities, based on historical data, to determine the specialty of an arriving patient. The proportion of sessions in the session roster determines the probability that a patient is assigned to a specialist, which differs from reality. There is no exchange of patients between specialists. Furthermore, we use a probability that a patient has the age of 12 years or younger per specialty, which is information we use for determining sequence of an OR program. All these probabilities are given in Appendix A.

From historical data, we identify 277 different surgery types, based on the surgery code, for which there are at least 20 performed surgeries. From this data, we determine for each surgery type a 3-parameter lognormal distribution by minimizing the Mean Squared Error (MSE). Surgery types with an MSE higher than 0.004, four in total, are excluded. We make a trade-off between including many different surgery types and the smallest MSE as possible, by choosing this MSE as threshold. Figure 4.3 shows the MSEs of all surgery types (every surgery type has a position on the y-axis). We use the same data for the case-mix plot in Figure 2.6. In the data, there are many surgery types with less than 20 performed surgeries, and therefore not included in the simulation model (see Section 2.7). 13% of all surgeries are excluded in the simulation model. The surgery types of these surgeries have longer average surgery durations than the 277 surgery types we use in the model, which means there is a discrepancy of the overall average duration between the simulation and reality. To reduce this difference, we perform a correction to the parameter γ of the 3-parameter lognormal distribution of the surgery duration. The magnitude of the correction depends on the patient type, elective or emergent, and specialty, so that the average surgery duration per specialty of the simulation model does not differ from the reality. However, this could cause differences between reality and simulation on the surgery type level. Appendix A gives the corrections per specialty. We use the mean of the surgery types as the booked durations.

0,0% 1,0% 2,0% 3,0% 4,0% 5,0% 6,0% 7,0% 8,0% 9,0% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Perc en ta ge o f to ta l

hour of the day

Arrival of emergency patients

44 Figure 4.3: Mean Squared Errors of surgery duration distributions

4.1.3.

Starts and changeovers

As input for the surgery durations, changeovers, and starts (late and early) we use 3-parameter lognormal distributions. We use one distribution per OR for changeovers, and also one distribution per OR for the starts. Distributions for surgery durations are per surgery type. Appendix A shows the parameters and MSE of these distributions.