Using simulation in out patient queues a case study

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International Journal of Health Care Quality Assurance9/6 [1996] 21–25© MCB University Press [ISSN 0952-6862]

Using simulation in out-patient queues: a case study

Fenghueih HuarngNational Chung Cheng University, Chia-Yi, TaiwanMong Hou LeeNational Chung Cheng University, Chia-Yi, Taiwan

Overwork and overcrowding insome periods was an impor-tant issue for the out-patientdepartment of a local hospitalin Chia-Yi in Taiwan. Thehospital administratorswanted to manage the patientflow effectively. Describes astudy which focused on theutilization of doctors and staffin the out-patient depart-ment, the time spent in thehospital by an out-patient,and the length of the out-patient queue. Explains how acomputer simulation modelwas developed to study howchanges in the appointmentsystem, staffing policies andservice units would affect theobserved bottleneck. Theresults show that the waitingtime was greatly reduced andthe workload of the doctorwas also reduced to a reason-able rate in the overwork andovercrowding periods.

IntroductionAs a result of the rapid growth of the econ-omy and the availability of education for allin Taiwan, the people of Taiwan have startedto demand more efficient health care at areasonable cost, and with better quality ofservice. The new insurance policy for every-one in Taiwan, the evaluation systemimposed on all hospitals by the Department ofHealth, and increasing severe competitionwithin the industry, are some of the issuesforcing Taiwan’s hospitals to improve theirquality of service and operational effective-ness. As hospitals raise their technical qual-ity, patients will lay more emphasis on qual-ity assurance. In order to survive, most ofTaiwan’s hospitals are making efforts toimprove their service quality to satisfy theirpatients.

There are many indicators of quality assur-ance. In the out-patient department, the mainindicator of quality assurance for patients is“waiting” itself; patients should be attendedto within an acceptable time. In Taiwan mosthospitals do not give their patients timedappointments, but instead issue a sequencingnumber. Therefore, most patients suffer along wait.

In this case history, the utilization of doc-tors and staff in the out-patients department,the time spent in the hospital by the out-patient, and the length of the out-patientqueue is studied for a small local hospital atChia-yi in Taiwan. Using the simulationtechnique, some suggestions for improve-ment are presented to help the hospitaladjust their operations to reduce the waitingtime and improve quality assurance in theout-patient department.

Literature reviewThe waiting problem is listed as one of theindicators of quality assurance for the healthcare system in several papers[1-3]. Jackson[4]proposes two main principles for schedulingpatients in out-patient departments. First, thescheduled time slot between two patientsdepends on the average consultation time ofeach physician. The best ratio of average

consultation time to scheduled time slotbetween two patients is from 0.85 to 0.95. Sec-ond, it is better for the time point to be inmultiples of five minutes. Welch[5] considerspunctuality and consultation time as twomain factors affecting the scheduling systemfor an out-patient department. Because manypatients are unsure about the time of theirappointment, they tend to arrive earlier thanthey should; hence, their waiting timesincrease. In addition, because many physi-cians are late, patients’ waiting timesincrease even more. Rising et al.[6] proposeda new scheduling system. First, allocate theconsultation time to patients who turn upwithout an appointment. Then, the remain-ing time slots are scheduled to patients byappointment so that the out-patients’ waitingtime is reduced and the physicians’ over-running time is reduced too.

Allessandra et al.[7] study the efficiency of afamily planning clinic and propose severalalternatives for improvement to reduce thelength of the queues and increase the utiliza-tion of physicians. Vassilacopoulos[8] allocates doctors to several shifts accordingto the patients’ arrival rate in an accident andemergency department. Babes and Sarma[9]study the out-patient queues of Ibn-RochdHealth Centre and compare the advantagesand disadvantages of using queuing modelsand simulation techniques.

For other hospital operation problems, see [10-18].

The out-patient service before improvementsThe various functions of the out-patientdepartment of the case hospital include regis-tration, general practice medicine, a cashdesk (patients are charged on-site for treat-ment), pharmacy (the drugstore is inside inthe hospital in Taiwan), immunology, and lab.The manager of the case hospital told us themost serious problem in the out-patientdepartment is overcrowding in the dermatol-ogy clinic. The patients’ waiting time in der-matology is so long that the waiting area isnot large enough to accommodate the queue.Staff in dermatology feel tired when they are

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Fenghueih Huarng andMong Hou LeeUsing simulation in out-patient queues: a case studyInternational Journal of Health Care Quality Assurance9/6 [1996] 21–25

under pressure, but in other sections thereare fewer patients and staff are not very busy.

In order to have real data instead of per-sonal, subjective impressions, the averagenumber of patients at each session was col-lected and categorized according to differentsessions and different allocations of physi-cians and staff. Six models, including differ-ent sessions, different numbers of physicians,different numbers of cashiers, and the aver-age number of patients are listed in Table I.Table I shows that dermatology is the bottle-neck, but the average number of patients perhour in models III, V and VI is smaller (82/8 =10.25, 80/8 = 10, and 104/12 = 8.7 respectively).In other words, apart from model IV, there arefewer patients in the afternoon.

Because it was difficult to record everypatient’s waiting time at each function (thewaiting time for consulting a physician, thewaiting time for paying for treatment, etc.),we collected only the service times andpatients’ inter-arrival times for simulation,and the waiting time at each function couldbe estimated from the results of the simula-tion. In this case study, the service time foreach function was recorded for 30 days duringDecember 1992 to January 1993. The arrivaltime of each patient was set to be the end ofhis/her registration time, as it was hard toverify and collect the exact time of thepatient’s arrival at the case hospital, and boththe registration time and the queue lengthare quite short in the case hospital. Hence, inthis case study, the registration function isexcluded from the out-patient system.

When the data were collected, the meaninter-arrival times on the Wednesday after-noon and on the Saturday afternoon weresuspected to be different. First, each

inter-arrival time was matched against theexponential distribution. Since the sample sizewas about 200, a Z-test was conducted to checkthe difference between two means. The Z valueis 0.696 which is less than Z0.95 (= 1.645), hence,the inter-arrival times for Wednesday after-noon and Saturday afternoon are combined tobe exponentially distributed with 2.28 min-utes of average inter-arrival time for modelIV. There are another 125 patients who registered on each Wednesday and Saturdaymorning for dermatology (the patients registered in advance represent only about 5 per cent for the other programme). Theservice time is matched against an appropri-ate distribution and listed in Table II.

In order to study the out-patient flow formodel IV, the number of simulations run onthe SLAM system[19] is 1,000 using the abovedata on arrival and service processes. Inmodel IV, there are two physicians – one isresponsible for both general medicine andgeneral surgery, the other treats the patientsin dermatology – one nurse responsible forimmunizations, one pharmacist, and fourpathologists responsible for different jobs inthe lab. The results of the simulation arelisted in Table III. To validate the simulationmodel, the results shown in Table III are con-sistent with the views of managers and staffof the out-patient department, and the aver-age number of patients served in simulation,333, compares with the actual average num-ber of patients, 335; the error rate is 0.6 percent.

From Table III, it is shown that the queuingproblem is acceptable, since the time spent inthe system for those patients in general medi-cine and general surgery is 20.1 minutes (only17.6 per cent of patients had to wait above half

Table IThe average number of patients in each model

Number of Number of Average numberModel Session Programme physicians cashiers of patientsI Mon. Wed. Sat. GM, GS, 2 2 90

(Morning) SkeletologyII 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 104Notes:Morning: 8.00 a.m.-12 noon; afternoon: 2.00 p.m.-10 p.m.GM = general medicine; GS = general surgery

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an hour). However, the waiting time for thosepatients in dermatology is 30.59 minutes, thetime in the system being 37.9 minutes (13.0per cent of patients had to wait above 1.5hours). The average consulting time for eachpatient in dermatology is quite short (only1.82 minutes). Most of the time, patients indermatology do not need the services of thelab and immunology, and it takes only 1.10minutes and 1.18 minutes for the averageservice time spent at the cash desk and in thepharmacy. Hence, most of the time spent inthe system for patients in dermatology is forwaiting. This is not a good indicator for qual-ity assurance. Moreover, the utilization rateof physicians in dermatology is 0.96 per cent,which is quite high. The maximum busy timecould be as long as eight hours. Usually, for aneight-hour period of work, there is at least ahalf-hour break. Hence, the working load istoo high for a physician. Currently the wait-ing area available is designed for 20 people,but the simulation results show that the max-imum queue is 36, which is much larger thanthe capacity. Therefore, model IV does needsome action to improve the current condi-tions.

Suggestions for improvement There are two main ways to change the queu-ing problems. One is to change the arrivalprocess, the other is to change the serviceprocess[20]. In this study, we propose twoalternatives. First, change the arrivalprocess, that is, increase the number ofpatients who make an appointment. Accord-ing to Jackson’s[4] suggestion, the ratio ofconsulting time between two consecutivepatients to time slot between two consecutiveappointments is set to be 0.95. When all thepatients are scheduled by appointment andall patients are assumed to arrive on time,patients in general medicine and generalsurgery are influenced to some extent; timein the system is decreased from 20.1 minutesto 16.61 minutes, and the time in system forpatients in dermatology is reduced to only17.42 minutes, along with a large reduction inthe maximum queue (the new queue is 14patients). Moreover, the average number ofpatients served is 242, which is only ten fewerthan the original model IV. Although it isimpossible to limit the number of patientswithout appointments and those who do notarrive in time for their appointments[6], it is

Table IIIThe results of simulation for model IV

Departmental performance GM and GS Dermatology Cash desk Laboratory Pharmacy ImmunologyAverage waiting time (minutes) 2.42 30.59 0.24 0.0 2.58 2.57Average queue (number of parients) 0.42 13.91 0.14 0.0 2.02 0.33Max. queue (number of parients) 6 36 5 0.0 12 5Average utilization 0.47 0.96 0.76 0.30 0.75 0.48Average No. of patients served 81 252 338 11 369 60Max. idle time (minutes) 66.94 28.61 – – 15.81 113.11Max. busy time (minutes) 198.45 480.0 – – 353.16 211.04Notes: Average time in system for patients in GM and GS 20.1 minutesAverage time in system for patients in dermatology 37.9 minutes

Table IIDistributions of service time and their associated parametersService Sample size Distribution ParametersGeneral medicine 212 Exponential MAR = 0.3597General surgery 49 Exponential MAR = 0.3546Skeletology 48 Exponential MAR = 0.3571Dermatology 129 Exponential MAR = 0.5495Cash desk 413 Lognormal Mean = 1.10

SD = 1.20Laboratory 63 Normal Mean = 13.30

SD = 2.80Pharmacy 501 Exponential MAR = 0.8475Immunology 294 Exponential MAR = 0.2703Notes:MAR = mean arrival rate (patient served per hour)SD = standard deviation

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almost certain that the overall waiting time isreduced when the ratio of appointment tonon-appointment patients is large. The imple-mentation of the appointment systemrequires the agreement of staff in the depart-ment of medical records. Unfortunately, thestaff in this department are not willing tomake more effort to implement the appoint-ment system.

The second approach is to change the ser-vice process. There are two options to makingthis change. One is to bring in one new physi-cian with specialty in dermatology onWednesday afternoons or Saturday after-noons. The other is to find another session tohave the current physician practising indermatology. The first option is not appropri-ate because of the following two reasons.First, recruiting could be a big problem; sec-ond, there would be more patients on theWednesday afternoon or Saturday afternoonto increase the workload of the pharmacywhose current utilization rate is already 76per cent. Incidentally, the high workload ofthe physician in dermatology implies that thephysician is popular with the patients andtherefore they would prefer to be referred tothis same physician. Therefore, the secondoption is better. There are only two consult-ing rooms available. It is better not to add aphysician into a session which currently hastwo physicians, and Sunday is not a normalworking day for the physician. Hence, thebest option is to extend the current physicianin dermatology to one afternoon of model III.According to Worthington’s[21] empiricalstudy, it is shown that, as the supplyincreases, the demand increases. This iscalled “feedback”. In other words, as supplyincreases, the demand does not increase untilthe queuing reaches the level before theincrease of supply. However, in this study, wethink the above feedback could be reachedonly if the supply is highly insufficient. It isassumed that the patients in dermatologywill increase about 20 per cent if the casehospital extends the current physician in

dermatology to one afternoon of model III.Therefore, there are 255 × 2 = 510 patients inevery week; after the increase of 20 per cent,the average number of patients in dermatol-ogy per week becomes 612. It is assumed thatthe 612 is divided into three afternoons. Thereare 204 patients in each afternoon in derma-tology. Also, it is assumed that there are125/255 = 49 per cent of patients who registerin the same morning to be first in the queueto see a doctor. Then the average inter-arrivaltime becomes 2.61 minutes. The simulationresults are shown in Table IV.

From Table IV, the average time in the sys-tem for patients in dermatology is reducedfrom 37.9 minutes to 19.9 minutes (only 3 percent of patients whose time in system isgreater than 1.5 hours, 17.6 per cent ofpatients whose time in the system is abovehalf an hour). The improvement in waitingtime is evident. The maximum queue lengthis reduced from 36 to 13 (the average queuelength is reduced from 13.91 to 3.78) such thatwaiting space is not a problem any more. Theutilization rate of physicians in dermatologyis reduced to 78 per cent such that the physi-cian is at less risk of making erroneous diag-noses due to fatigue and is able to concentrateon providing quality consultation time toeach patient in turn. The satisfaction ofphysicians in dermatology could be higherwith his/her workload reduced to a reason-able rate. Since the decrease of the number ofpatients in dermatology will not increase theworkload of the other services in the out-patient department, the case hospital addedan extra session for dermatology patients onMonday afternoons at the end of 1993. Thetotal number of patients in dermatologyevery month from March 1994 to May 1994(the average number of patients per week isshown in parentheses) is listed in Table V.From Table V, it is shown that patients gradu-ally shift to the new section (Monday after-noon). The managers and staff of the out-patient department of the case hospital haveall shown their satisfaction with the changes.

Table IVThe results of simulation for model IV (assume 20 per cent of increase)

Departmental performance GM and GS Dermatology Cash desk Laboratory Pharmacy ImmunologyAverage waiting time (minutes) 2.29 8.4 0.15 0.0 1.96 2.94Average queue (number of patients) 0.54 3.78 0.09 0.0 1.29 0.6Max. queue (number of patients) 6 13 4 0.0 10 5Average utilization 0.48 0.78 0.66 0.30 0.67 0.48Average no. of patients served 83 206 296 11 334 65Max. idle time (minutes) 58.22 50.04 – – 28.0 106.80Max. busy time (minutes) 243.78 455.62 – – 300.16 247.45Notes:Average time in system for patients in GM and GS 19.3 minutesAverage time in system for patients in dermatology 19.9 minutes

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ConclusionIn this case study, the out-patient departmentwas analysed, and the most overcrowdedsessions (model IV) were simulated to studythe patients’ queue and service utilization ofstaff. It is obvious that, before the improve-ment, the high workload of the physician indermatology should be changed by increas-ing the available consultation time of thephysician. The simulation was used to solvethe remaining problems of how much theconsultation time should be increased andhow the change would affect the currentsystem. A few alternatives were proposed toimprove the queuing problem in model IVwith the simulation results. The case hospitalchose the option of adding an extra session ofdermatology on Monday afternoons. Theresults show that the total number of patientsincreased, which is consistent withWorthington’s[21] “feedback” theory. Thequeue length was reduced considerably andthe patients’ average waiting time wasreduced by 18 minutes in dermatology.

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Table VOutpatient number in dermatology

Monday Wednesday SaturdayMarch 450(112) 459(115) 691(138)April 771(154) 718(180) 619(155)May 716(179) 1013(203) 880(220)Notes:( ) indicates the average out-patient number in eachafternoon

Health & Medicine

Using simulation in out patient queues a case study