Results of the Simulation Model

Having developed a simulation model of the CCU based on actual data and having validated some key outcomes of the model, it can now be utilised as an operational research tool.

The final result consists of comparing the bed occupancy profile from the data with the output from the model. The model is run with 29 beds available. This resulted in 74% bed occupancy utilisation rate compared with observed rate of 75%. Recall that on 1.32% of occasions there were more than 29 beds occupied. In the simulation model it appeared that on 2.27% of occasions bed occupancy was higher than 29, and in fact there were as many as 36 patients at any one time. The main reason for this is the same as in the data, patients are allowed to queue on trolleys if the hospital staff know there will be a bed available in the CCU shortly.

The measures that are examined are: mean and standard deviation of bed occupancy. The mean and the standard deviation of bed occupancy, according to the data, was 21.85 and 3.65 respectively, compared with 21.51 and 4.28 respectively, according to the simulation. The results of the simula- tion model are compared with the data and are presented in Figure 3.5.

The bed occupancy distribution displayed in Figure 3.5 is comparable with the actual bed occu- pancy profile, and hence it is concluded that the simulation model provides a reasonably accurate representation of the real-life CCU activities. However, the simulation model overestimates the low bed occupancy (between 0 and 18) and high bed occupancy (between 27 and 35) and under- estimates mid-valued bed occupancy, which is the reason for a slightly higher standard deviation comparing with the actual data. In order to investigate that variation in bed occupancy further,

Chapter 3 MATHEMATICAL MODELLING OF THE CCUAT THE UHW 49

Figure 3.5: Distribution of bed occupancy

several ‘what if’ scenarios will be considered.

3.2.3

‘What if’ Scenario #1

The previous section detailed some initial results of the simulation model; however, no major alter- nations were made to the model; arrival rates and duration of stay remained unchanged.

This section will examine the effect of implementing some new policies regarding cancellation of elective surgeries. As has been previously mentioned, the CCU has an insufficient number of beds to accommodate demand on all occasions, and sometimes elective surgeries may require cancella- tion. Recall that the main method of control over the rate of admissions to the CCU is by means of changing the admission rates of elective patients. A principle of the design of the simulation model is that it does not allow any elective admissions when bed occupancy reaches high levels. A point at which elective arrivals are beginning to be cancelled will be called the ‘cut-off’ point. Since the number of funded beds in the CCU is 24, when bed occupancy is 24 or higher no elective admissions are allowed. The proposed rule for the cancellation of elective procedures during busy periods is incorporated into the model. If on any one day after admitting priority emergency pa- tients, the number of occupied beds was greater or equal to 24, the number of elective admissions was set to zero. It means that all planned elective surgeries for that day are cancelled and those patients are lost to the system, since in this model no queueing is allowed.

The effect of that ‘what if’ scenario is highly influential. The measures that were again examined are: mean and standard deviation of bed occupancy. The mean number and the standard deviation of bed occupancy, according to the simulation, is 20.24 and 3.73 respectively. Unsurprisingly, the average bed occupancy is now lower than in the data, since the model does not allow as many elective admissions as previously. This is shown in Figure 3.6.

Chapter 3 MATHEMATICAL MODELLING OF THE CCUAT THE UHW 50

Figure 3.6: Distribution of number of elective admissions with cut-off at 24

Clearly, the percentage of days when there were no elective admissions is very high (64%) and the effect on bed occupancy is presented in Figure 3.7.

Figure 3.7: Distribution of bed occupancy with cut-off at 24

High bed occupancies are no longer overestimated by simulation, but clearly the proportion of low bed occupancy is overestimated. This would be undesirable since each bed is a very expensive and limited resource, and there are many people who have to wait to be admitted to the CCU for post-operative treatment. Also, if for example, there are 20 nurses employed per shift and only ten beds are occupied, there is potential for a large wastage in nursing cost. To rectify this problem a second ’what if’ scenario is considered.

The implication of changes in the mode of operation of the CCU is now considered. Recall also that the main method of control over the rate of admissions to the CCU is by means of changing

Chapter 3 MATHEMATICAL MODELLING OF THE CCUAT THE UHW 51 the admission rates of elective patients. Recall that two of the principal aims of this study are to increase the throughput of patients, and to reduce the variation in bed occupancy levels on a day-to-day basis, so that more stability may be observed in the numbers of nurses needed per shift.

3.2.4

‘What if’ Scenario #2

The second ‘what if’ scenario investigates the effect of increasing the number of elective admissions by up to 4 per day whenever there are less than 24 beds occupied. That is, whenever there appears to be sufficient spare bed capacity, then allowing extra (up to four) elective patients to be admitted is suggested. For example, if there are currently 22 beds occupied, only two extra elective patients would be allowed, since the cut-off at 24 beds. However, if there are 20 or less beds in use four extra admissions are allowed. The question arose: is it realistic to expect patients facing elective surgery to have that surgery brought forward at short notice (typically three days)? Discussions with clinical staff indicate that this indeed may be possible. For example, transplant patients are aware that they may be called for surgery at a very short notice if a donated organ becomes available. Likewise, it may be possible to set up a pool of patients waiting for more general surgery, with agreement reached beforehand with patients that their surgery may be performed sooner if they agree to join the pool for call-up at three days or so notice.

Figure 3.8: Distribution of bed occupancy with cut-off at 24 and extra elective admissions at non- busy times

The results of the simulation model are compared with the data and are illustrated in Figure 3.8. Visibly, very low and very high bed occupancy levels are no longer overestimated and mid-valued bed occupancy levels are higher than in the actual data. The mean bed occupancy increases to 22.6, a 3.5% increase and the standard deviation is reduced to 3.00, a 17.8% decrease. The variation of bed occupancy levels on a day-to-day basis was reduced significantly, which makes the system more stable and decisions regarding the number of nurses needed per shift are easier to make. The

Chapter 3 MATHEMATICAL MODELLING OF THE CCUAT THE UHW 52 throughput is increased from 1406 to 1473 patients per year, a 4.8% increase. Thus, a relatively mi- nor increase in admissions of elective patients at non-busy times shows a improvement in variability and throughput at no extra cost to the hospital.

3.2.5

Conclusions

The principal objective of this section was to develop a model that is sufficiently detailed mathe- matically and easily comprehensible to hospital managerial staff. It is believed that this objective has been achieved. Detailed analyses of arrival and length of stay profiles, presented in Section 2.3, provided results of the simulation model of the CCU that correspond relatively well with the actual CCU data.

Consider now a theoretical approach, whose objectives are the same as of the simulation model.