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   181 AN APPLICATION OF QUEUING ANALYSIS TO THE “WAITINGROOM” PROBLEM IN THE HOSPITAL ADMISSIONS PROCESS   Igor Georgievskiy, Zhanna Georgievskaya, & Wm. PinneyAlcorn State University MBA Program(601)304-4376 ABSTRACT This paper examines the Admissions process in a regional hospital with the purpose of documenting the existing process and its bottleneck points, determining the waiting timedistributions at the two waiting room settings within the system, and developingrecommendations for modifying the layout and staffing of the system to reduce waiting times forpatients.Data were recorded for arrival into the system (waiting time 1 (WT1)), and transition fromcheck-in to financial arrangements processing (waiting time 2 (WT2)) followed by departurefrom the system (to a specialty unit or out of the system). The flow charts for the admissionprocess are shown.A facility layout analysis provided a proposed redesign of patient flow and changed the numberof work stations to alleviate choke points in the system, a proposed scheduling strategyevaluation provided new arrival rate figures, and queuing analysis was employed to predict theimprovements in waiting times. BACKGROUND The Admissions process in a regional hospital was examined with the purpose of documentingthe existing process and its bottleneck points, determining the waiting time distributions, anddeveloping recommendations for modifying the layout and staffing of the system to reducewaiting times for patients.Data were recorded for arrival into the system (Source: AD Sign-in log, Tracking Sheets),transition from sign-in to admitting arrangements processing (i.e. waiting in the waiting area),arrival to the registration desk (Source: AD Sign-in log, Tracking Sheets, Hospital InformationSystem (Meditech)), and departure from the system to a specialty unit or out of the system(Tracking Sheets). The patient flows and waiting areas are depicted in Figure 1. The number of servers, the average time in the system, and the average time in the queue for the existingstaffing levels are shown in Table 1 and Figure 2.In our study, modified M/M/s queuing model was used. A classic M/M/s, or Erlang delay model,assumes a single queue with unlimited waiting room that feeds into s identical servers.Customers arrive according to a Poisson process with a constant rate and the service duration hasan exponential distribution (Hall 1990). In healthcare, the Poisson process has been identified asan optimal representation of unscheduled arrivals to various systems (Kim et al 1999, Green et al2005). Since in our case the majority of out-patient non-emergent visits were not scheduled we   182used the Poisson distribution for arrival process in the models. After an extensive statisticalanalysis of the collected data, it was determined that the service rate had a Poisson distribution aswell.Since the M/M/s model assumes that the arrival rate does not change over the day, to model oursystem (that had a fluctuating arrival rate) we used the M/M/s model as a part of a SIPP(stationary independent period-by-period) approach to determine how to vary staff to meetchanging demand. The SIPP approach starts with dividing the day into staffing periods, then aseries of M/M/s models are constructed. After that, each of these periods is separately analyzedand solved for optimal number of servers to meet the target service requirements (Green 2006).In our study, the day was divided into 12 periods: 10 1-hour periods and 2 ½-hour periods. Thisdivision was used for all models we developed (Table 1). REDUCING WAITING TIME There are several possible ways of improving patient flow, and thereby reducing waiting time forthe patients. These include (1) Increasing the number of servers; (2) Managing the arrival rate;and (3) Optimizing the service rate.The number of servers can be increased by hiring more admitting clerks. This is the mostobvious by not necessarily the best decision. Although increasing the number of servers providesimmediate results (Table 2 and Figure 3), the most effective approach to improvement shouldinvolve optimization of all three variables mentioned above. The arrival rate should be decreased during busy times and increased during “slow” periods. Scheduling arrivals would modify thearrival rate to the necessary degree.Implementation of an online Appointment Management System would allow scheduling of non-emergency outpatient visits. Radiology was selected to be the first department to test thesoftware. When the hospital starts using the scheduling system to its full extent, the arrival rate inthe AD is expected to be stabilized significantly. It was assumed that having implementedappointment software and having been using it for several months, the hospital will be able toschedule over 90% of outpatient Radiology visits. The current arrival rate of the Radiologypatients is depicted in Figure 4, along with the impact of this change on the overall arrival ratefor the AD (see also Table 3). The impact of combining these modifications in staffing andarrival rate on the average time in the system and the queue are shown in Table 4 and Figure 5.The third key variable that can affect system patient flow is service rate. It can be decreased byvarious means: pre-registering a larger number of patients, introducing a patient member plastic card which would contain patient’s demographic information, using electronic medical forms rather than paper-based, optimizing admitting clerk work place layout (the survey of currentoperations revealed that on average, each admitting clerk visits the work room 2-4 times whileserving a patient to make copies, fax documents and so on; providing personal office equipmentwill eliminate the need of visiting the work room while serving the patient) and so forth.   183 RECOMMENDATIONS This study attempted to analyze actual operations of a hospital and proposed modifications in thesystem to reduce waiting times for the patients, which should lead to an improved view of thequality of service provided. Three areas of change were recommended: (1) increasing thenumber and rescheduling the work times of the admissions clerks, (2) adopting an AppointmentManagement System to spread the arrivals into the system and avoid unacceptable levels of inputs at certain times of the day, and (3) increasing the service rate of the clerks byimplementing electronically based systems for pre-registration, re-registration, and documentreproduction functions.Any changes should be evaluated by computer based systems employing queuing analysis andby simulation studies to predict the efficacy of the proposed modifications, prior to their actualimplementation. The current study is a first step in that direction. REFERENCES Green, L.V., 2006, “Queuing Analysis in Healthcare”, Patient Flow: Reducing Delay in Healthcare Delivery. Springer Science + Business Media, LLC: 281-307; Green, L.V., Giulio, J., Green, R., and Soares, J., 2005, “Using Queuing Theory to Increase the Effectiveness of Physician Staffing in the Em ergency Department”, Academic Emergency Medicine, Volume 13, Issue1: 61-68;Hall, R.W., 1990, Queuing Methods for Service and Manufacturing. Mew Jersey: Prentice Hall; Kim, S., Horowitz, I., Young, K.K., and Buckley, T.A., 1999, “Analysis of Capacity Man agement of the Intensive Care Unit in a Hospital”. European Journal of Operational Research, 115: 36-46.     184 Start Patent logs inAD clerk  verifies patient’s registrationAdmittingclerk isavailable?NoYesPatient waspre-registered?YesNoYesNoPatient waitsin the waitingarea Chart 1A. Patient Flow in the Admitting Department, with Waiting Time Patient arrives to theAdmitting Department(AD)Registrationverified? To A (chart 1B) AD clerk verifies patient’s personal information   Patient hasan accountat NRMC?AD clerk collectspersonal informationNoYesAD clerk creates  patient’s profile Front-desk clerk isavailable?NoYes   Patient waitsin the waitingareaPersonalinfoverified?NoYesYesAD clerk corrects  patient’s personal info Patient arrivesto the booth WT 1 CHARTS, TABLES AND FIGURES:   185 AD Clerk tries tolocate the order callingto other departments (chart 1B)(chart 1B) Orderis confirmed/ corrected To E (chart 1C) Yes Physician’s office isavailable?No To D (chart 1C) AD clerk calls the  physician’s officeNoDiagnosisspecification/ correction isneeded?YesOrder isfaxed toADYesNeed tocorrect theorder?NoYesOrderisfound?NoNoInsuranceisverified ?  NoOrder isfound?AD Clerk tries tolocate the orderin the ADFinancialconsulting isneeded?NoFinancialconsultingis startedEndof registrationYesYesYesNoPt waits inthe waitingareaNoInsuranceverificationPt waits inthe waitingareaNo YesNoYesYesInsuranceverificationis needed? Physician’s order is ok? B CA YesNeed tolocate theorder?Financialconsultant isavailable? F Issue isresolved?YesFinancialconsultingis providedCan ADclerk provideconsulting?Issue isresolved?NoNoYesYesNo    W   T   2 (chart 1B) B   C   B   Chart 1B. Patient Flow in the Admitting Department, with Waiting Time
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