2. Fenghueih Huarng and under pressure, but in other sections there inter-arrival time was matched against the
Mong Hou Lee are fewer patients and staff are not very busy . exponential distribution. Since the sample size
Using simulation in out- In order to have real data instead of per- was about 200, a Z-test was conducted to check
patient queues: a case study sonal, subjective impressions, the average the difference between two means. The Z value
International Journal of number of patients at each session was col- is 0.696 which is less than Z0.95 (= 1.645), hence,
Health Care Quality lected and categorized according to different the inter-arrival times for Wednesday after-
Assurance
sessions and different allocations of physi- noon and Saturday afternoon are combined to
9/6 [1996] 21â25
cians and staff. Six models, including differ- be exponentially distributed with 2.28 min-
ent sessions, different numbers of physicians, utes of average inter-arrival time for model
different numbers of cashiers, and the aver- IV There are another 125 patients who
.
age number of patients are listed in Table I. registered on each Wednesday and Saturday
Table I shows that dermatology is the bottle- morning for dermatology (the patients
neck, but the average number of patients per registered in advance represent only about
hour in models III, V and VI is smaller (82/8 = 5 per cent for the other programme). The
10.25, 80/8 = 10, and 104/12 = 8.7 respectively). service time is matched against an appropri-
In other words, apart from model IV there are
, ate distribution and listed in Table II.
fewer patients in the afternoon. In order to study the out-patient ïŹow for
Because it was difficult to record every model IV the number of simulations run on
,
patientâs waiting time at each function (the the SLAM system[19] is 1,000 using the above
waiting time for consulting a physician, the data on arrival and service processes. In
waiting time for paying for treatment, etc.), model IV there are two physicians â one is
,
we collected only the service times and responsible for both general medicine and
patientsâ inter-arrival times for simulation, general surgery, the other treats the patients
and the waiting time at each function could in dermatology â one nurse responsible for
be estimated from the results of the simula- immunizations, one pharmacist, and four
tion. In this case study, the service time for pathologists responsible for different jobs in
each function was recorded for 30 days during the lab. The results of the simulation are
December 1992 to January 1993. The arrival listed in Table III. To validate the simulation
time of each patient was set to be the end of model, the results shown in Table III are con-
his/her registration time, as it was hard to sistent with the views of managers and staff
verify and collect the exact time of the of the out-patient department, and the aver-
patientâs arrival at the case hospital, and both age number of patients served in simulation,
the registration time and the queue length 333, compares with the actual average num-
are quite short in the case hospital. Hence, in ber of patients, 335; the error rate is 0.6 per
this case study, the registration function is cent.
excluded from the out-patient system. From Table III, it is shown that the queuing
When the data were collected, the mean problem is acceptable, since the time spent in
inter-arrival times on the Wednesday after- the system for those patients in general medi-
noon and on the Saturday afternoon were cine and general surgery is 20.1 minutes (only
suspected to be different. First, each 17.6 per cent of patients had to wait above half
Table I
The average number of patients in each model
Number of Number of Average number
Model Session Programme physicians cashiers of patients
I Mon. Wed. Sat. GM, GS, 2 2 90
(Morning) Skeletology
II Tues. Thurs. Fri. GM, GS, 2 2 67
(Morning)
III Mon. Tues. Fri. GM, GS, 1 1 82
(Afternoon)
IV Wed. Sat. GM, GS, 2 2 335
(Afternoon) Dermatology (225 for
dermatology)
V Thurs. GM, GS, 2 1 80
(Afternoon) Skeletology
VI Sun. GM, GS, 1 1 104
Notes:
Morning: 8.00 a.m.-12 noon; afternoon: 2.00 p.m.-10 p.m.
GM = general medicine; GS = general surgery
[ 22 ]
3. Fenghueih Huarng and Table II
Mong Hou Lee Distributions of service time and their associated parameters
Using simulation in out-
patient queues: a case study Service Sample size Distribution Parameters
International Journal of General medicine 212 Exponential MAR = 0.3597
Health Care Quality General surgery 49 Exponential MAR = 0.3546
Assurance Skeletology 48 Exponential MAR = 0.3571
9/6 [1996] 21â25
Dermatology 129 Exponential MAR = 0.5495
Cash desk 413 Lognormal Mean = 1.10
SD = 1.20
Laboratory 63 Normal Mean = 13.30
SD = 2.80
Pharmacy 501 Exponential MAR = 0.8475
Immunology 294 Exponential MAR = 0.2703
Notes:
MAR = mean arrival rate (patient served per hour)
SD = standard deviation
an hour). However, the waiting time for those
patients in dermatology is 30.59 minutes, the Suggestions for improvement
time in the system being 37.9 minutes (13.0 There are two main ways to change the queu-
per cent of patients had to wait above 1.5 ing problems. One is to change the arrival
hours). The average consulting time for each process, the other is to change the service
patient in dermatology is quite short (only process[20]. In this study, we propose two
1.82 minutes). Most of the time, patients in alternatives. First, change the arrival
dermatology do not need the services of the process, that is, increase the number of
lab and immunology, and it takes only 1.10 patients who make an appointment. Accord-
minutes and 1.18 minutes for the average ing to Jacksonâs[4] suggestion, the ratio of
service time spent at the cash desk and in the consulting time between two consecutive
pharmacy Hence, most of the time spent in
. patients to time slot between two consecutive
the system for patients in dermatology is for appointments is set to be 0.95. When all the
patients are scheduled by appointment and
waiting. This is not a good indicator for qual-
all patients are assumed to arrive on time,
ity assurance. Moreover, the utilization rate
patients in general medicine and general
of physicians in dermatology is 0.96 per cent,
surgery are inïŹuenced to some extent; time
which is quite high. The maximum busy time
in the system is decreased from 20.1 minutes
could be as long as eight hours. Usually, for an
to 16.61 minutes, and the time in system for
eight-hour period of work, there is at least a patients in dermatology is reduced to only
half-hour break. Hence, the working load is 17.42 minutes, along with a large reduction in
too high for a physician. Currently the wait- the maximum queue (the new queue is 14
ing area available is designed for 20 people, patients). Moreover, the average number of
but the simulation results show that the max- patients served is 242, which is only ten fewer
imum queue is 36, which is much larger than than the original model IV Although it is
.
the capacity Therefore, model IV does need
. impossible to limit the number of patients
some action to improve the current condi- without appointments and those who do not
tions. arrive in time for their appointments[6], it is
Table III
The results of simulation for model IV
Departmental performance GM and GS Dermatology Cash desk Laboratory Pharmacy Immunology
Average waiting time (minutes) 2.42 30.59 0.24 0.0 2.58 2.57
Average queue (number of parients) 0.42 13.91 0.14 0.0 2.02 0.33
Max. queue (number of parients) 6 36 5 0.0 12 5
Average utilization 0.47 0.96 0.76 0.30 0.75 0.48
Average No. of patients served 81 252 338 11 369 60
Max. idle time (minutes) 66.94 28.61 â â 15.81 113.11
Max. busy time (minutes) 198.45 480.0 â â 353.16 211.04
Notes:
Average time in system for patients in GM and GS 20.1 minutes
Average time in system for patients in dermatology 37.9 minutes
[ 23 ]
4. Fenghueih Huarng and almost certain that the overall waiting time is dermatology to one afternoon of model III.
Mong Hou Lee reduced when the ratio of appointment to Therefore, there are 255 Ă 2 = 510 patients in
Using simulation in out- non-appointment patients is large. The imple- every week; after the increase of 20 per cent,
patient queues: a case study mentation of the appointment system the average number of patients in dermatol-
International Journal of requires the agreement of staff in the depart- ogy per week becomes 612. It is assumed that
Health Care Quality ment of medical records. Unfortunately, the the 612 is divided into three afternoons. There
Assurance
9/6 [1996] 21â25
staff in this department are not willing to are 204 patients in each afternoon in derma-
make more effort to implement the appoint- tology Also, it is assumed that there are
.
ment system. 125/255 = 49 per cent of patients who register
The second approach is to change the ser- in the same morning to be ïŹrst in the queue
vice process. There are two options to making to see a doctor. Then the average inter-arrival
this change. One is to bring in one new physi- time becomes 2.61 minutes. The simulation
cian with specialty in dermatology on results are shown in Table IV .
Wednesday afternoons or Saturday after- From Table IV the average time in the sys-
,
noons. The other is to ïŹnd another session to tem for patients in dermatology is reduced
have the current physician practising in from 37.9 minutes to 19.9 minutes (only 3 per
dermatology The ïŹrst option is not appropri-
. cent of patients whose time in system is
ate because of the following two reasons. greater than 1.5 hours, 17.6 per cent of
First, recruiting could be a big problem; sec- patients whose time in the system is above
ond, there would be more patients on the half an hour). The improvement in waiting
Wednesday afternoon or Saturday afternoon time is evident. The maximum queue length
to increase the workload of the pharmacy is reduced from 36 to 13 (the average queue
whose current utilization rate is already 76 length is reduced from 13.91 to 3.78) such that
per cent. Incidentally, the high workload of waiting space is not a problem any more. The
the physician in dermatology implies that the utilization rate of physicians in dermatology
physician is popular with the patients and is reduced to 78 per cent such that the physi-
therefore they would prefer to be referred to cian is at less risk of making erroneous diag-
this same physician. Therefore, the second noses due to fatigue and is able to concentrate
option is better. There are only two consult- on providing quality consultation time to
ing rooms available. It is better not to add a each patient in turn. The satisfaction of
physician into a session which currently has physicians in dermatology could be higher
two physicians, and Sunday is not a normal with his/her workload reduced to a reason-
working day for the physician. Hence, the able rate. Since the decrease of the number of
best option is to extend the current physician patients in dermatology will not increase the
in dermatology to one afternoon of model III. workload of the other services in the out-
According to Worthingtonâs[21] empirical patient department, the case hospital added
study, it is shown that, as the supply an extra session for dermatology patients on
increases, the demand increases. This is Monday afternoons at the end of 1993. The
called âfeedbackâ. In other words, as supply total number of patients in dermatology
increases, the demand does not increase until every month from March 1994 to May 1994
the queuing reaches the level before the (the average number of patients per week is
increase of supply However, in this study, we
. shown in parentheses) is listed in Table V .
think the above feedback could be reached From Table V it is shown that patients gradu-
,
only if the supply is highly insufficient. It is ally shift to the new section (Monday after-
assumed that the patients in dermatology noon). The managers and staff of the out-
will increase about 20 per cent if the case patient department of the case hospital have
hospital extends the current physician in all shown their satisfaction with the changes.
Table IV
The results of simulation for model IV (assume 20 per cent of increase)
Departmental performance GM and GS Dermatology Cash desk Laboratory Pharmacy Immunology
Average waiting time (minutes) 2.29 8.4 0.15 0.0 1.96 2.94
Average queue (number of patients) 0.54 3.78 0.09 0.0 1.29 0.6
Max. queue (number of patients) 6 13 4 0.0 10 5
Average utilization 0.48 0.78 0.66 0.30 0.67 0.48
Average no. of patients served 83 206 296 11 334 65
Max. idle time (minutes) 58.22 50.04 â â 28.0 106.80
Max. busy time (minutes) 243.78 455.62 â â 300.16 247.45
Notes:
Average time in system for patients in GM and GS 19.3 minutes
Average time in system for patients in dermatology 19.9 minutes
[ 24 ]
5. Fenghueih Huarng and Table V outpatient clinicâ, Operations Research, Vol.
Mong Hou Lee Outpatient number in dermatology 21, 1973, pp. 1030-47.
Using simulation in out- 7 Allessandra, A.J., Grazman,T.E., Parames-
patient queues: a case study Monday Wednesday Saturday waran, R. and Yavas, U., âUsing simulation in
International Journal of hospital planningâ, Simulation, Vol. 30, 1978,
March 450(112) 459(115) 691(138)
Health Care Quality pp. 62-7.
April 771(154) 718(180) 619(155)
Assurance 8 Vassilacopoulos, G., âAllocating doctors to
9/6 [1996] 21â25 May 716(179) 1013(203) 880(220) shifts in an accident and emergency depart-
Notes: mentâ, Journal of Operational Research
( ) indicates the average out-patient number in each Society, Vol. 36 No. 6, 1985, pp. 517-23.
afternoon 9 Babes, M. and Sarma,G.V âOut-patient
.,
queues at the Ibn-Rochd Health Centreâ, Jour-
nal of the Operational Research Society, Vol. 42
No. 10, 1991, pp. 845-55.
Conclusion 10 Dumas, M.B., âHospital bed utilization: an
implemented simulation approach to adjusting
In this case study, the out-patient department and maintaining appropriate levelsâ, Health
was analysed, and the most overcrowded Service Research, Vol. 20 No. 1, 1985, pp. 43-61.
sessions (model IV) were simulated to study 11 Gupta, T., âUse of simulation technique in
the patientsâ queue and service utilization of maternity care analysisâ, Computers Industry
staff. It is obvious that, before the improve- Engineering, Vol. 21, 1991, pp. 489-93.
ment, the high workload of the physician in 12 Kwak, N.K., Kuzdrall P.J. and Schmitz, H.H.,
dermatology should be changed by increas- âThe GPSS simulation of scheduling policies
for surgical patientsâ, Management Science,
ing the available consultation time of the
Vol. 22 No. 9, 1976, pp. 982-9.
physician. The simulation was used to solve
13 Mahachek, A.R. and Knabe, T.L., âComputer
the remaining problems of how much the simulation of patient ïŹow in obstetrical/
consultation time should be increased and gynecology clinicsâ, Simulation, Vol. 43, 1984,
how the change would affect the current pp. 95-101.
system. A few alternatives were proposed to 14 Pallin, A. and Kittell, R.P., âMercy Hospital:
improve the queuing problem in model IV simulation techniques for ER processesâ,
with the simulation results. The case hospital Industrial Engineering, Vol. 24 No. 2, 1992,
chose the option of adding an extra session of pp. 35-7.
dermatology on Monday afternoons. The 15 Rakich, J.S., Kuzdrall, P.J., Klafehn, K.A. and
Krigline, A.G., âSimulation in the hospital
results show that the total number of patients
setting: implications for managerial decision
increased, which is consistent with
making and management developmentâ, Jour-
Worthingtonâs[21] âfeedbackâ theory The . nal of Management Development, Vol. 10 No. 4,
queue length was reduced considerably and 1991, pp. 31-7.
the patientsâ average waiting time was 16 Romanin-Jacur, G. and Facchin, P., âOptimal
reduced by 18 minutes in dermatology . planning of a pediatric semi-intensive care
unit via simulationâ, European Journal of
References Operational Research, Vol. 29, 1987, pp. 192-8.
1 Fisher, A.W., âPatientsâ evaluation of outpa- 17 Vassilacopoulos, G., âA simulation model for
tient medical careâ, Journal of Medical Educa- bed allocation to hospital inpatient depart-
tion, Vol. 46, 1971. mentsâ, Simulation, Vol. 45 No. 5, 1985,
2 Hyde, P.C., âSetting standards in health careâ, pp. 233-41.
Quality Assurance, Vol. 12 No. 2, 1986. 18 Wilt, A. and Goddin, D., âHealth care case
3 Sasser, W.E., Olsen, R.P. and Wyckoff, D.D., study: simulation staffing needs and work ïŹow
Management of Service Operations-Text, Cases, in an outpatient diagnostic centerâ, Industrial
and Readings, Allyn & Bacon, Boston, MA, Engineering, Vol. 21 No. 5, 1989, pp. 22-26.
1978. 19 Pritsker, A.A.B., Introduction to Simulation
4 Jackson, R.R.P., âDesign of an appointments and SLAM II, John Wiley & Son, New York, NY,
systemâ, Operational Research Quarterly, Vol. 1986.
15, 1964, pp. 219-24. 20 Hall, R.W., Queuing Methods for Services and
5 Welch, J.D., âAppointment systems in hospital Manufacturing, Prentice-Hall, Englewood
outpatient departmentsâ, Operational Cliffs, NJ, 1991.
Research Quarterly, Vol. 15, 1964, pp. 224-32. 21 Worthington, D.J., âQueuing models for hospi-
6 Rising, E.J., Baron, R. and Averill, B.,âA tal waiting listsâ, Journal of Operational
systems analysis of a university-health-service Research Society, Vol. 38 No. 5, 1987, pp. 413-22.
[ 25 ]