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Using simulation in out-patient queues: a case study


                                   Fenghueih Huarng
                                   National Chung Cheng University, Chia-Yi, Taiwan
                                   Mong Hou Lee
                                   National Chung Cheng University, Chia-Yi, Taiwan


Overwork and overcrowding in                                                         consultation time to scheduled time slot
some periods was an impor-          Introduction                                     between two patients is from 0.85 to 0.95. Sec-
tant issue for the out-patient     As a result of the rapid growth of the econ-      ond, it is better for the time point to be in
department of a local hospital     omy and the availability of education for all     multiples of five minutes. Welch[5] considers
in Chia-Yi in Taiwan. The          in Taiwan, the people of Taiwan have started      punctuality and consultation time as two
hospital administrators            to demand more efficient health care at a         main factors affecting the scheduling system
wanted to manage the patient       reasonable cost, and with better quality of       for an out-patient department. Because many
flow effectively. Describes a       service. The new insurance policy for every-      patients are unsure about the time of their
study which focused on the         one in Taiwan, the evaluation system              appointment, they tend to arrive earlier than
utilization of doctors and staff   imposed on all hospitals by the Department of     they should; hence, their waiting times
in the out-patient depart-         Health, and increasing severe competition         increase. In addition, because many physi-
ment, the time spent in the        within the industry, are some of the issues       cians are late, patients’ waiting times
hospital by an out-patient,        forcing Taiwan’s hospitals to improve their       increase even more. Rising et al.[6] proposed
and the length of the out-         quality of service and operational effective-     a new scheduling system. First, allocate the
patient queue. Explains how a      ness. As hospitals raise their technical qual-    consultation time to patients who turn up
computer simulation model          ity, patients will lay more emphasis on qual-     without an appointment. Then, the remain-
was developed to study how         ity assurance. In order to survive, most of       ing time slots are scheduled to patients by
changes in the appointment         Taiwan’s hospitals are making efforts to          appointment so that the out-patients’ waiting
system, staffing policies and      improve their service quality to satisfy their    time is reduced and the physicians’ over-
service units would affect the     patients.                                         running time is reduced too.
observed bottleneck. The
                                     There are many indicators of quality assur-       Allessandra et al.[7] study the efficiency of a
results show that the waiting
                                   ance. In the out-patient department, the main     family planning clinic and propose several
time was greatly reduced and
                                   indicator of quality assurance for patients is    alternatives for improvement to reduce the
the workload of the doctor
                                   “waiting” itself; patients should be attended     length of the queues and increase the utiliza-
was also reduced to a reason-
                                   to within an acceptable time. In Taiwan most      tion of physicians. Vassilacopoulos[8]
able rate in the overwork and
                                   hospitals do not give their patients timed        allocates doctors to several shifts according
overcrowding periods.
                                   appointments, but instead issue a sequencing      to the patients’ arrival rate in an accident and
                                   number. Therefore, most patients suffer a         emergency department. Babes and Sarma[9]
                                   long wait.                                        study the out-patient queues of Ibn-Rochd
                                     In this case history, the utilization of doc-   Health Centre and compare the advantages
                                   tors and staff in the out-patients department,    and disadvantages of using queuing models
                                   the time spent in the hospital by the out-        and simulation techniques.
                                   patient, and the length of the out-patient          For other hospital operation problems,
                                   queue is studied for a small local hospital at    see [10-18].
                                   Chia-yi in Taiwan. Using the simulation
                                   technique, some suggestions for improve-
                                   ment are presented to help the hospital            The out-patient service
                                   adjust their operations to reduce the waiting     before improvements
                                   time and improve quality assurance in the
                                                                                     The various functions of the out-patient
                                   out-patient department.
                                                                                     department of the case hospital include regis-
                                                                                     tration, general practice medicine, a cash
                                                                                     desk (patients are charged on-site for treat-
                                    Literature review
                                                                                     ment), pharmacy (the drugstore is inside in
                                   The waiting problem is listed as one of the       the hospital in Taiwan), immunology, and lab.
                                   indicators of quality assurance for the health    The manager of the case hospital told us the
                                   care system in several papers[1-3]. Jackson[4]    most serious problem in the out-patient
International Journal of           proposes two main principles for scheduling       department is overcrowding in the dermatol-
Health Care Quality
Assurance                          patients in out-patient departments. First, the   ogy clinic. The patients’ waiting time in der-
9/6 [1996] 21–25                   scheduled time slot between two patients          matology is so long that the waiting area is
© MCB University Press             depends on the average consultation time of       not large enough to accommodate the queue.
[ISSN 0952-6862]                                                                     Staff in dermatology feel tired when they are
                                   each physician. The best ratio of average
                                                                                                                               [ 21 ]
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] 21–25
                               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 flow for
                                 Because it was difficult to record every                 model IV the number of simulations run on
                                                                                                    ,
                               patient’s 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 – one is
                                                                                                    ,
                               we collected only the service times and                    responsible for both general medicine and
                               patients’ inter-arrival times for simulation,              general surgery, the other treats the patients
                               and the waiting time at each function could                in dermatology – 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-
                               patient’s 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 ]
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] 21–25
                                 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 Jackson’s[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 influenced 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                –              –           15.81            113.11
Max. busy time (minutes)                    198.45                480.0                –              –          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 ]
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 × 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] 21–25
                                 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 first 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 find 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 first 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 Worthington’s[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 “feedback”. 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            –                –           28.0            106.80
Max. busy time (minutes)                  243.78             455.62           –                –          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 ]
Fenghueih Huarng and           Table V                                                      outpatient clinic”, 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., “Using simulation in
International Journal of                                                                    hospital planning”, 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., “Allocating doctors to
9/6 [1996] 21–25               May            716(179)      1013(203)       880(220)        shifts in an accident and emergency depart-
                               Notes:                                                       ment”, 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 “Out-patient
                                                                                                                          .,
                                                                                            queues at the Ibn-Rochd Health Centre”, Jour-
                                                                                            nal of the Operational Research Society, Vol. 42
                                                                                            No. 10, 1991, pp. 845-55.
                                Conclusion                                             10    Dumas, M.B., “Hospital bed utilization: an
                                                                                            implemented simulation approach to adjusting
                               In this case study, the out-patient department               and maintaining appropriate levels”, 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., “Use of simulation technique in
                               the patients’ queue and service utilization of               maternity care analysis”, 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-                    “The GPSS simulation of scheduling policies
                                                                                            for surgical patients”, 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., “Computer
                               the remaining problems of how much the                       simulation of patient flow in obstetrical/
                               consultation time should be increased and                    gynecology clinics”, 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., “Mercy Hospital:
                               improve the queuing problem in model IV                      simulation techniques for ER processes”,
                               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., “Simulation in the hospital
                               results show that the total number of patients
                                                                                            setting: implications for managerial decision
                               increased, which is consistent with
                                                                                            making and management development”, Jour-
                               Worthington’s[21] “feedback” theory The .                    nal of Management Development, Vol. 10 No. 4,
                               queue length was reduced considerably and                    1991, pp. 31-7.
                               the patients’ average waiting time was                  16   Romanin-Jacur, G. and Facchin, P., “Optimal
                               reduced by 18 minutes in dermatology      .                  planning of a pediatric semi-intensive care
                                                                                            unit via simulation”, European Journal of
                               References                                                   Operational Research, Vol. 29, 1987, pp. 192-8.
                                1 Fisher, A.W., “Patients’ evaluation of outpa-        17   Vassilacopoulos, G., “A simulation model for
                                  tient medical care”, Journal of Medical Educa-            bed allocation to hospital inpatient depart-
                                  tion, Vol. 46, 1971.                                      ments”, Simulation, Vol. 45 No. 5, 1985,
                                2 Hyde, P.C., “Setting standards in health care”,           pp. 233-41.
                                  Quality Assurance, Vol. 12 No. 2, 1986.              18   Wilt, A. and Goddin, D., “Health care case
                                3 Sasser, W.E., Olsen, R.P. and Wyckoff, D.D.,              study: simulation staffing needs and work flow
                                  Management of Service Operations-Text, Cases,             in an outpatient diagnostic center”, 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., “Design of an appointments               and SLAM II, John Wiley & Son, New York, NY,
                                  system”, Operational Research Quarterly, Vol.             1986.
                                  15, 1964, pp. 219-24.                                20   Hall, R.W., Queuing Methods for Services and
                                5 Welch, J.D., “Appointment systems in hospital             Manufacturing, Prentice-Hall, Englewood
                                  outpatient departments”, Operational                      Cliffs, NJ, 1991.
                                  Research Quarterly, Vol. 15, 1964, pp. 224-32.       21   Worthington, D.J., “Queuing models for hospi-
                                6 Rising, E.J., Baron, R. and Averill, B.,“A                tal waiting lists”, Journal of Operational
                                  systems analysis of a university-health-service           Research Society, Vol. 38 No. 5, 1987, pp. 413-22.




                                                                                                                                       [ 25 ]

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Using simulation in out patient queues a case study

  • 1. Using simulation in out-patient queues: a case study Fenghueih Huarng National Chung Cheng University, Chia-Yi, Taiwan Mong Hou Lee National Chung Cheng University, Chia-Yi, Taiwan Overwork and overcrowding in consultation time to scheduled time slot some periods was an impor- Introduction between two patients is from 0.85 to 0.95. Sec- tant issue for the out-patient As a result of the rapid growth of the econ- ond, it is better for the time point to be in department of a local hospital omy and the availability of education for all multiples of five minutes. Welch[5] considers in Chia-Yi in Taiwan. The in Taiwan, the people of Taiwan have started punctuality and consultation time as two hospital administrators to demand more efficient health care at a main factors affecting the scheduling system wanted to manage the patient reasonable cost, and with better quality of for an out-patient department. Because many flow effectively. Describes a service. The new insurance policy for every- patients are unsure about the time of their study which focused on the one in Taiwan, the evaluation system appointment, they tend to arrive earlier than utilization of doctors and staff imposed on all hospitals by the Department of they should; hence, their waiting times in the out-patient depart- Health, and increasing severe competition increase. In addition, because many physi- ment, the time spent in the within the industry, are some of the issues cians are late, patients’ waiting times hospital by an out-patient, forcing Taiwan’s hospitals to improve their increase even more. Rising et al.[6] proposed and the length of the out- quality of service and operational effective- a new scheduling system. First, allocate the patient queue. Explains how a ness. As hospitals raise their technical qual- consultation time to patients who turn up computer simulation model ity, patients will lay more emphasis on qual- without an appointment. Then, the remain- was developed to study how ity assurance. In order to survive, most of ing time slots are scheduled to patients by changes in the appointment Taiwan’s hospitals are making efforts to appointment so that the out-patients’ waiting system, staffing policies and improve their service quality to satisfy their time is reduced and the physicians’ over- service units would affect the patients. running time is reduced too. observed bottleneck. The There are many indicators of quality assur- Allessandra et al.[7] study the efficiency of a results show that the waiting ance. In the out-patient department, the main family planning clinic and propose several time was greatly reduced and indicator of quality assurance for patients is alternatives for improvement to reduce the the workload of the doctor “waiting” itself; patients should be attended length of the queues and increase the utiliza- was also reduced to a reason- to within an acceptable time. In Taiwan most tion of physicians. Vassilacopoulos[8] able rate in the overwork and hospitals do not give their patients timed allocates doctors to several shifts according overcrowding periods. appointments, but instead issue a sequencing to the patients’ arrival rate in an accident and number. Therefore, most patients suffer a emergency department. Babes and Sarma[9] long wait. study the out-patient queues of Ibn-Rochd In this case history, the utilization of doc- Health Centre and compare the advantages tors and staff in the out-patients department, and disadvantages of using queuing models the time spent in the hospital by the out- and simulation techniques. patient, and the length of the out-patient For other hospital operation problems, queue is studied for a small local hospital at see [10-18]. Chia-yi in Taiwan. Using the simulation technique, some suggestions for improve- ment are presented to help the hospital The out-patient service adjust their operations to reduce the waiting before improvements time and improve quality assurance in the The various functions of the out-patient out-patient department. department of the case hospital include regis- tration, general practice medicine, a cash desk (patients are charged on-site for treat- Literature review ment), pharmacy (the drugstore is inside in The waiting problem is listed as one of the the hospital in Taiwan), immunology, and lab. indicators of quality assurance for the health The manager of the case hospital told us the care system in several papers[1-3]. Jackson[4] most serious problem in the out-patient International Journal of proposes two main principles for scheduling department is overcrowding in the dermatol- Health Care Quality Assurance patients in out-patient departments. First, the ogy clinic. The patients’ waiting time in der- 9/6 [1996] 21–25 scheduled time slot between two patients matology is so long that the waiting area is © MCB University Press depends on the average consultation time of not large enough to accommodate the queue. [ISSN 0952-6862] Staff in dermatology feel tired when they are each physician. The best ratio of average [ 21 ]
  • 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] 21–25 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 flow for Because it was difficult to record every model IV the number of simulations run on , patient’s 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 – one is , we collected only the service times and responsible for both general medicine and patients’ inter-arrival times for simulation, general surgery, the other treats the patients and the waiting time at each function could in dermatology – 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- patient’s 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] 21–25 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 Jackson’s[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 influenced 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 – – 15.81 113.11 Max. busy time (minutes) 198.45 480.0 – – 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 × 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] 21–25 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 first 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 find 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 first 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 Worthington’s[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 “feedback”. 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 – – 28.0 106.80 Max. busy time (minutes) 243.78 455.62 – – 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 clinic”, 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., “Using simulation in International Journal of hospital planning”, 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., “Allocating doctors to 9/6 [1996] 21–25 May 716(179) 1013(203) 880(220) shifts in an accident and emergency depart- Notes: ment”, 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 “Out-patient ., queues at the Ibn-Rochd Health Centre”, Jour- nal of the Operational Research Society, Vol. 42 No. 10, 1991, pp. 845-55. Conclusion 10 Dumas, M.B., “Hospital bed utilization: an implemented simulation approach to adjusting In this case study, the out-patient department and maintaining appropriate levels”, 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., “Use of simulation technique in the patients’ queue and service utilization of maternity care analysis”, 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- “The GPSS simulation of scheduling policies for surgical patients”, 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., “Computer the remaining problems of how much the simulation of patient flow in obstetrical/ consultation time should be increased and gynecology clinics”, 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., “Mercy Hospital: improve the queuing problem in model IV simulation techniques for ER processes”, 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., “Simulation in the hospital results show that the total number of patients setting: implications for managerial decision increased, which is consistent with making and management development”, Jour- Worthington’s[21] “feedback” theory The . nal of Management Development, Vol. 10 No. 4, queue length was reduced considerably and 1991, pp. 31-7. the patients’ average waiting time was 16 Romanin-Jacur, G. and Facchin, P., “Optimal reduced by 18 minutes in dermatology . planning of a pediatric semi-intensive care unit via simulation”, European Journal of References Operational Research, Vol. 29, 1987, pp. 192-8. 1 Fisher, A.W., “Patients’ evaluation of outpa- 17 Vassilacopoulos, G., “A simulation model for tient medical care”, Journal of Medical Educa- bed allocation to hospital inpatient depart- tion, Vol. 46, 1971. ments”, Simulation, Vol. 45 No. 5, 1985, 2 Hyde, P.C., “Setting standards in health care”, pp. 233-41. Quality Assurance, Vol. 12 No. 2, 1986. 18 Wilt, A. and Goddin, D., “Health care case 3 Sasser, W.E., Olsen, R.P. and Wyckoff, D.D., study: simulation staffing needs and work flow Management of Service Operations-Text, Cases, in an outpatient diagnostic center”, 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., “Design of an appointments and SLAM II, John Wiley & Son, New York, NY, system”, Operational Research Quarterly, Vol. 1986. 15, 1964, pp. 219-24. 20 Hall, R.W., Queuing Methods for Services and 5 Welch, J.D., “Appointment systems in hospital Manufacturing, Prentice-Hall, Englewood outpatient departments”, Operational Cliffs, NJ, 1991. Research Quarterly, Vol. 15, 1964, pp. 224-32. 21 Worthington, D.J., “Queuing models for hospi- 6 Rising, E.J., Baron, R. and Averill, B.,“A tal waiting lists”, Journal of Operational systems analysis of a university-health-service Research Society, Vol. 38 No. 5, 1987, pp. 413-22. [ 25 ]