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Using simulation in out patient queues a case study

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  • 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, TaiwanOverwork and overcrowding in consultation time to scheduled time slotsome 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 indepartment of a local hospital omy and the availability of education for all multiples of five minutes. Welch[5] considersin Chia-Yi in Taiwan. The in Taiwan, the people of Taiwan have started punctuality and consultation time as twohospital administrators to demand more efficient health care at a main factors affecting the scheduling systemwanted to manage the patient reasonable cost, and with better quality of for an out-patient department. Because manyflow effectively. Describes a service. The new insurance policy for every- patients are unsure about the time of theirstudy which focused on the one in Taiwan, the evaluation system appointment, they tend to arrive earlier thanutilization of doctors and staff imposed on all hospitals by the Department of they should; hence, their waiting timesin 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 timeshospital by an out-patient, forcing Taiwan’s hospitals to improve their increase even more. Rising et al.[6] proposedand the length of the out- quality of service and operational effective- a new scheduling system. First, allocate thepatient queue. Explains how a ness. As hospitals raise their technical qual- consultation time to patients who turn upcomputer 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 bychanges in the appointment Taiwan’s hospitals are making efforts to appointment so that the out-patients’ waitingsystem, 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 aresults show that the waiting ance. In the out-patient department, the main family planning clinic and propose severaltime was greatly reduced and indicator of quality assurance for patients is alternatives for improvement to reduce thethe 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 accordingovercrowding 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-patientInternational Journal of proposes two main principles for scheduling department is overcrowding in the dermatol-Health Care QualityAssurance 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 theMong Hou Lee are fewer patients and staff are not very busy . exponential distribution. Since the sample sizeUsing simulation in out- In order to have real data instead of per- was about 200, a Z-test was conducted to checkpatient queues: a case study sonal, subjective impressions, the average the difference between two means. The Z valueInternational 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 to9/6 [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 IIMong Hou Lee Distributions of service time and their associated parametersUsing simulation in out-patient queues: a case study Service Sample size Distribution ParametersInternational Journal of General medicine 212 Exponential MAR = 0.3597Health Care Quality General surgery 49 Exponential MAR = 0.3546Assurance Skeletology 48 Exponential MAR = 0.35719/6 [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 isTable IIIThe results of simulation for model IVDepartmental 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 [ 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 inUsing 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 thatHealth Care Quality ment of medical records. Unfortunately, the the 612 is divided into three afternoons. ThereAssurance9/6 [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 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[ 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 inInternational 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 to9/6 [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 ]