Hourly bed census model

For the input for the bed census model we used the data as described in Appendix A. Since we use a cycle of 7 days (S andRare 7 (Section 4.1.2), soQequals 7), we only use data from January 1 2014 to December 29 2015 to make sure we have an equal number of observations per patient type. The number of admissions and average LOS of this period is shown in Table 5.1. For the arrival distribution we left out the 5 weeks per year where ZGT reduced the number of beds because of holidays, since the arrivals during this period significantly differ from the rest of the year. This leaves us with 104 observations for the LOS distributions for each patient type and 94 observations for the arrival distributions.

Table 5.1: Input data used.

# admissions Average LOS Elective patiens 354 2.38 days Acute patients 1143 4.24 days

The arrival, surgery, admission day, admission time, discharge day and discharge time distributions are estimated per patient type, as described in Section 4.1.2. We defined a total of 7 elective patient types and 168 acute patient types. We also mentioned in Section 4.1.2 that we do not differentiate between surgery specialties, so we do not need several ORs and only consider one OR. In Table 5.2 some of the input for the bed census model is shown.

5.1. Model input

Table 5.2: Input hourly bed census model.

Parameter Description Value

Q Number of days in cycle 7

T Number of timeslots in a day 24

I Number of operating rooms 1

K Number of units 2

M Number of total beds 16

J Set of patient types 175

From the historical data, the maximum LOS equals 84 days. The maximum number of elective patients arriving during a day is 3 and the maximum number of acute patients arriving per hour is 2. The maximum time where an elective patient is ad- mitted is 20.00h. In Appendix D the input for bi,s and the Poisson arrival rates for

acute patients are shown. For the arrival distribution, we did not only want to take into account the realized admissions, but also the rejected patients. In Table 2.1 we saw that the rejection rate was 3.23% in the years 2014 and 2015, so we multiplied the arrivals for both elective and acute patients with 1.0323. Whether this method is valid for modeling the arrivals is shown in Section 5.2.

As discussed in Section 4.1.2, elective patients can not be admitted the day before surgery, only the day of surgery. The probabilities for cj(k), wjn,t, Pj(n) and m

j n,t

are shown in Appendix D. The discharge time, mj_n,t, is determined separately for when a patient is discharged during its first or second day on the ICU, but after the second day, the discharge time distribution is the same for all days up to the maximum LOS.

5.1.2

Nurse staffing model

The input data to the nurse staffing model are shown in Table 5.3. The shifts start at 7.00h, 15.00h and 23.00h, to align the shifts with the hourly bed census model. The ratios r_q,τk are as described in Table 2.2. For the desired overall service level we choose 95% and for the desired minimum service level 75%. This means that in case of 1 unit of 16 beds, there will always be sufficient staff for 12 patients and in case of a unit of 8 beds, there will always be sufficient staff for 6 patients. Since we were not able of getting a good indication of the costs for a temporary nurse, we vary the costs from twice as much as a contracted nurse to four times as much.

Table 5.3: Input nurse staffing model.

Parameter Description Value

Mk Bed-capacity unit k [8,8]

T Set of shift types 3

bτ Start time slot of shift τ [7,15,23]

yτ Length in time slot of shift τ [8,8,8]

rq,τI,k Patient-nurse ratio for shift (q, τ) on wardkin case of intenisve care

Chapter 5. Experimental design

rq,τM,k Patient-nurse ratio for shift (q, τ) on wardkin case of medium care

[2.5,2.75,3]

αk Desired overall service level per shift at unitk 95%

βk Desired minimum service level per time slot at unitk 75%

γk Desired minimum fraction of dedicated nurses on ward

k

2/3

wd Staffing costs for each dedicated nurse who is staffed for one shift

1

wf Staffing costs for each float nurse who is staffed for one shift

1

wt Staffing costs for each temporary nurse who is staffed for one shift

[2,3,4]

5.1.3

Simulation model

As described in Section 4.3.1, we use the input for the hourly bed census model as well for the simulation model. We only change the input, when differentiating MCU-patients from the ICU-patients. As discussed in Section 3.3, a patient is of the ICU-category when in need of respiratory support or dialysis. Otherwise, the patient is of the MCU-category. From historical data we used the start of ventilator support or dialysis from patients as the start of ICU-stay and the end of MCU-stay. Vice versa for the end of ventilator support or dialysis.

The LOS for the time until the next transition or until discharge for patients in the simulation model is only dependent of whether the LOS is a MCU-stay or a ICU-stay. In this distribution no more difference between the elective patients and acute patients is made, as described in Section 4.3.1 to obtain reliable LOS dis- tributions. However, upon arrival the probability of arriving as a MCU-patient or a ICU-patient is dependent of the patient being an elective or acute patient. As described in Section 4.3.1 the number of transitions between complexities of care depends on whether the patients is elective or acute, and whether the patient belong to the ICU or MCU-category upon arrival.

Since the LOS-distribution for either MCU or ICU-stay is determined from historical data, all transitions that occurred in the years 2014 and 2015 are used. However, in the data a lot of LOSs were of a duration less than an hour, as a patient either arrives to the ICU not on respiratory support, but does require it half an hour later, or a transition between the two complexities is of a short duration. Since all these probabilities of a LOS less than an hour are not possible in the bed census model, as patients arrive at the start of an hour and can only be discharged at the end of the next hour, we merged these durations with the onces before or after. The input probabilities for the simulation model are shown in Appendix D.