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Delays and Waiting – a Challenge for Hospitals
DELAYS AND WAITING – A CHALLENGE FOR HOSPITALS
Analysis of an Out-Patient Service using Queueing Theory
Akilan Arunkumar.A, Research Scholar, Tata Institute of Social Sciences, Mumbai
Introduction
Health care providers are under a great deal of pressure to reduce costs and improve quality of services. In recent years, given the greater emphasis on preventive medicine and shorter lengths of stay, outpatient services are becoming an essential component of health care. Hospitals that cannot make their outpatient services more efficient and cost-effective find themselves in financially unviable positions in this fast-growing competitive industry.
Over the years, population has increased several folds and the greater demand and expectations of patients from hospitals are far more than what is currently being perceived. As a result, it has become a constant rat-race to make our current systems faster. This brings about questions such as how do we measure such improvements? Is there a standard procedure?
Today lot of research is taking place to make systems that provide critical life support to work faster. For example, the NHS has introduced performance specific targets which demands 98% of the patients enter an accident and emergency service unit, to be treated in less than 4 hours (response time).
Now the challenge is how to achieve such targets. The first thing that comes into mind is to increase the number of doctors and paramedics and the speed of the equipments in Hospitals. This would be possible if one has unlimited resources but, since this isn’t feasible in most of the cases, we would have to look at alternatives. In essence, the hospital could vary their limited number of staff at different departments according to the arrival rate and see what happens to the overall process time. However, this will prove to be time consuming and very expensive for the hospital and hence isn’t feasible.
This motivates to find appropriate models that would help us to simulate and predict the behaviour of an OPD. Various studies such as simulations, statistical modelling etc have been done in this area with all of them broadly based upon queuing theory. Since its inception by A.K Erlang in 1909, this has been the basis for modelling many different systems. If modeled accurately, not only will such a model give managers an insight into optimizing their resources, but will also show them which departments are bottlenecks.
The problem of waiting is recognized as one of the major challenges of many hospitals. This problem limits hospitals from serving population who are mostly busy and want to spend their valuable time productively. In an eye hospital where this study was carried out approximately it takes about 1 hour and thirty minutes to serve a patient.
Chart 1. Process time of patients from Jan- July 2006
Objective of the Study
(i) To determine the flow of patients and the time spent in the Hospital through arrival and service characteristics
(ii) To study the utilization of various servers
(iii) To understand the bottlenecks in the patient flow
(iv) To propose alternatives to make the patient flow process efficient with reduced waiting
Methodology
Therefore a study based on queueing principles was designed to know the arrival pattern of patients, the time taken to provide the service (service rate), and the utilization of ophthalmologists, optometrists and other staff involved in the OPD. According to queuing principles this OPD is a single channel- multiphase system with networks of such systems.
1413 samples were studied through this study. The response time was calculated from finding the difference between the entry and exit time. Data analysis was done using “QM for Windows” software.
Bottleneck Analysis
A bottleneck is the node(s) in the queueing network that has the highest utilisation. In other words it is a place where patients struck-up. Hence, when performing a bottleneck analysis for the different activities (nodes), we are trying to find the utilisation values for each node and ensure that this value never exceeds its capacity. If it does, then we will have to look at varying the parameters of this node namely the service rate and the number of servers (staffs) and see the effect that this change has on the overall response time of the system.
Bottlenecks
Chart.2. Server utilization values for different arrival rates
(Reg-Registration, RC-Preliminary check-up, Ref- Refraction, Cons-Consultation)
In this case, the bottleneck analysis reveals, where the system fails in ensuring quicker service. The above graph reveals that if more than 300 patients arrive to JEH OPD, queue starts building at reception centre. In the refraction system, when the arrivals are 350 to 400 the system exceeds the service capabilities and queue builds up.
Reception centre is the primary bottleneck, and Refraction closely follows that. This strengthens the argument that the congestion built in these two areas reflect on the other nodes and the system as a whole as well.
Solution for Bottlenecks
Reception centre with one and two servers
Parameter Present system
1 staff Proposed system
2 staff
Value Value
Average server utilization Steady
State
Violation 50 %
Average number in the queue(Lq) 0.333
Average number in the system(Ls) 1.333
Average time in the queue(Wq) 0.333
Average time in the system(Ws) 1.333
Table. 2. Reception centre with one and two servers
A mathematical simulation allows us to plan the service point requirements without any trial and error methods.
The above table depicts that the Reception centre system which was violating the steady state (beyond capacity) with one server was working at 50 per cent utlisation level and with less waiting with two servers. Which means adding up more staff could solve the Reception centre bottleneck.
Centralized preliminary screening area as a solution
1 2 3
Present System
(Technicians at
different places) One common refraction
(with same No. of technicians) One common refraction
(with reduced No. of technicians)
No. of technicians 8 8 6
Parameter Value Minutes Value Minutes Value Minutes
Average refraction server utilization 44% 48% 63%
Average number of patients in the queue(Lq) 0.55 0.04 0.41
Average patient in the Refraction chamber(Ls) 1.08 3.84 4.21
Average time in the queue for refraction(Wq) 4.75 285 0.05 3 0.54 32
Average time in the Refraction chamber(Ws) 9.75 585 5.05 303 5.54 332
Table.3 Centralized preliminary screening area as a solution
Having a centralized preliminary screening area with pooled technicians is another practical solution which increases the staff utilization with even less number of technicians.
The above table depicts that patients need to wait for lesser time comparing to the present system. Even with a reduced number of 6 technicians a higher utilization of 63 % is achieved with reduced waiting time (Column 3).
Discussions
• Since Reception centre being the primary bottleneck of the system, by increasing another server here, the system may be made to work in steady state.
• The possibility of clubbing function of Reception centre with the registration may also be explored since this could cut down one additional node and a total process time of 10 minutes approximately for each patient.
• However it was evidently proved through the simulations that having a single refraction chamber with 8 or even 6 technicians, the hospital could reduce waiting time up to 25 percent, as well as better utilization of resources.
Advanced simulations using simulators would help the administrators to visually see what happens when we change the resources in the system. In healthcare Queue modeling can be applied in the areas wherever queue is involved such as rationing, scheduling, Bed allocation, laboratory design, and so on.
REFERENCES
1. RANDOLPH W. HALL, The New Queueing theory for Healthcare, OR/MS Today, June 2006
2. JOHN G. CULLIS, PHILIP R. JONES AND CAROL PROPPER, “Waiting lists and medical treatment: Analysis and policies”, Chapter 23 in Handbook of Health Economics, 2000, vol. 1, pp 1201-1249, Elsevier
3. RISING, E., R. BARON, AND B. AVERILL (1973), “A System Analysis of a University Health Service Outpatient Clinic,” Operations Research, 21, 5, 1030-1047.
4. BABES, M. AND G. V. SARMA (1991), “Out-Patient Queues at the Ibn-Rochd Health Center,” Journal of the Operational Research Society, 42, 10, 845-855.
5. SWARTZMAN, G. (1970), “The Patient Arrival Process in Hospitals: Statistical Analysis,” Health Services Research, 5, 4, 320-329.
6. SUSAN L. ALBIN, JEFFREY BARRETT, DAVID ITO AND JOHN E. MUELLER, Queueing network analysis of a health center, Queueing Systems, Springer, Netherlands, Volume 7, Number 1 / March, 1990
About the Author
My graphing calculator isn’t showing Lin-Reg(ax+b) formula, how do i fix it?
Everytime i enter the points in L1 and L2, i cant ever get it to show the LinReg(ax+b) formula. How to i get it to show up on my Graphic Calculator. And i must mention that the Calculator is new.
To get the regression, go to Stat, right arrow key, and then 4: Lin-Reg. If you want the r value, go to [2nd] Catalog, then scroll down to DiagnosticOn, press Enter twice.
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