Patients arrive to a 24-hour, 7-days-a-week outpatient clinic with interarrival
ID: 457759 • Letter: P
Question
Patients arrive to a 24-hour, 7-days-a-week outpatient clinic with interarrival times being distributed as exponential with mean 5.95 (all times are in minutes); the first patient arrives at time 0. The clinic has five different stations (like nodes in a network), where patients might be directed for service before leaving. All patients first sign in with a single receptionist; sign-in times have a triangular distribution with parameters 1, 4, and 8. From here, there might go to the nurses’ station (Probability 0.9888) or to one of three exam rooms (Probability 0.0112). the table below gives the five stations, service times at those stations, and transaction Probabilities out of each station into the next station for a patient (including out of the sign-in station, just described as an example):
Next station probability (blank entries are zero probability)
Station
Service time
Sign In
Nurses’ station
Exam room
Lab and X-ray
Check out
Sign in
TRIA(1,4,8)
0.9888
0.0112
Nurses’ station
TRIA(2,5,7)
0.9167
0.0833
Exam room
TRIA(4,7,13)
0.0428
0.4706
0.0214
0.4652
Lab and X-ray
TRIA(15,23,38)
0.8333
0.1667
Check out
TRIA(3,5,8)
From check out, all patients leave and go home.
All Patients eventually go through the checkout station and go home. Note that it is possible that, after a visit to an exam room, a patient is directed to an exam room again (but may have to queue for it) after a patient Checks in but is queueing for either the nurses’ station or an exam room, regard patient as being in the waiting room (and those patients leaving an exam room but again directed to an exam room are also regarded as being in the waiting room). There are three identical exam rooms, but only one resource unit at each of the other four stations. Queues for each station are first-in, first-out, and we assume that movement time between stations is negligible. Run a simulation of round-the-clock24-hour days and observe the average total time in system of patients, the average number of patients present in the clinic, as well as the throughput of the clinic (number of patients who leave the clinic and go home over the 30 days); also make a plot of the number of patients present in the clinic, and display a throughput counter. If you could afford to add resources, where is the need most pressing? (see exercises 6-24 and 6-25 for better ways to address this question.)
This is a modification of a model developed by bretthauer and Cote (1998) and bretthauer (2000). The latter does an analytical evaluation and optimization under the assumption that this is a jackson network of queues, where service times also have exponential distributions (not triangular or other kinds of distribution). The advantage of simulating instead is that the model can be more general and thus possibly more valid; for instance, we do not have to assume exponential service times if the data suggest otherwise. The disadvantage of simulation is that we do not get exact answer, so we must do proper statistical analysis of the output (see Chapter 6). (Thanks to professor Jim Morris of the university of Wisconsin-Madison for suggesting these papers and this exercise.)
a) Make A general description of the problem and data used.
b) run an Arena models (Using Arena Rockwall Software) for the above case
Next station probability (blank entries are zero probability)
Station
Service time
Sign In
Nurses’ station
Exam room
Lab and X-ray
Check out
Sign in
TRIA(1,4,8)
0.9888
0.0112
Nurses’ station
TRIA(2,5,7)
0.9167
0.0833
Exam room
TRIA(4,7,13)
0.0428
0.4706
0.0214
0.4652
Lab and X-ray
TRIA(15,23,38)
0.8333
0.1667
Check out
TRIA(3,5,8)
From check out, all patients leave and go home.
Explanation / Answer
uidelines to Problem Solving and Decision Making
Much of what people do is solve problems and make decisions. Often, they are "under the gun", stressed and very short for time. Consequently, when they encounter a new problem or decision they must make, they react with a decision that seemed to work before. It's easy with this approach to get stuck in a circle of solving the same problem over and over again. Therefore, it's often useful to get used to an organized approach to problem solving and decision making. Not all problems can be solved and decisions made by the following, rather rational approach. However, the following basic guidelines will get you started. Don't be intimidated by the length of the list of guidelines. After you've practiced them a few times, they'll become second nature to you -- enough that you can deepen and enrich them to suit your own needs and nature.
(Note that it might be more your nature to view a "problem" as an "opportunity". Therefore, you might substitute "problem" for "opportunity" in the following guidelines.)
1. Define the problem
This is often where people struggle. They react to what they think the problem is. Instead, seek to understand more about why you think there's a problem.
Define the problem: (with input from yourself and others). Ask yourself and others, the following questions:
Defining complex problems:
If the problem still seems overwhelming, break it down by repeating steps 1-7 until you have descriptions of several related problems.
Verifying your understanding of the problems:
It helps a great deal to verify your problem analysis for conferring with a peer or someone else.
Prioritize the problems:
If you discover that you are looking at several related problems, then prioritize which ones you should address first.
Note the difference between "important" and "urgent" problems. Often, what we consider to be important problems to consider are really just urgent problems. Important problems deserve more attention. For example, if you're continually answering "urgent" phone calls, then you've probably got a more "important" problem and that's to design a system that screens and prioritizes your phone calls.
Understand your role in the problem:
Your role in the problem can greatly influence how you perceive the role of others. For example, if you're very stressed out, it'll probably look like others are, too, or, you may resort too quickly to blaming and reprimanding others. Or, you are feel very guilty about your role in the problem, you may ignore the accountabilities of others.
2. Look at potential causes for the problem
3. Identify alternatives for approaches to resolve the problem
At this point, it's useful to keep others involved (unless you're facing a personal and/or employee performance problem). Brainstorm for solutions to the problem. Very simply put, brainstorming is collecting as many ideas as possible, then screening them to find the best idea. It's critical when collecting the ideas to not pass any judgment on the ideas -- just write them down as you hear them. (A wonderful set of skills used to identify the underlying cause of issues is Systems Thinking.)
4. Select an approach to resolve the problem
(The nature of this step, in particular, in the problem solving process is why problem solving and decision making are highly integrated.)
5. Plan the implementation of the best alternative (this is your action plan)
(An important aspect of this step in the problem-solving process is continually observation and feedback.)
6. Monitor implementation of the plan
Monitor the indicators of success:
7. Verify if the problem has been resolved or not
One of the best ways to verify if a problem has been solved or not is to resume normal operations in the organization. Still, you should consider:
Rational Versus Organic Approach to Problem Solving
Rational
A person with this preference often prefers using a comprehensive and logical approach similar to the guidelines in the above section. For example, the rational approach, described below, is often used when addressing large, complex matters in strategic planning.
A major advantage of this approach is that it gives a strong sense of order in an otherwise chaotic situation and provides a common frame of reference from which people can communicate in the situation. A major disadvantage of this approach is that it can take a long time to finish. Some people might argue, too, that the world is much too chaotic for the rational approach to be useful.
Organic
Some people assert that the dynamics of organizations and people are not nearly so mechanistic as to be improved by solving one problem after another. Often, the quality of an organization or life comes from how one handles being “on the road” itself, rather than the “arriving at the destination.” The quality comes from the ongoing process of trying, rather than from having fixed a lot of problems. For many people it is an approach to organizational consulting. The following quote is often used when explaining the organic (or holistic) approach to problem solving.
“All the greatest and most important problems in life are fundamentally insoluble … They can never be solved, but only outgrown. This “outgrowing” proves on further investigation to require a new level of consciousness. Some higher or wider interest appeared on the horizon and through this broadening of outlook, the insoluble lost its urgency. It was not solved logically in its own terms, but faded when confronted with a new and stronger life urge.”
From Jung, Carl, Psychological Types (Pantheon Books, 1923)
A major advantage of the organic approach is that it is highly adaptable to understanding and explaining the chaotic changes that occur in projects and everyday life. It also suits the nature of people who shun linear and mechanistic approaches to projects. The major disadvantage is that the approach often provides no clear frame of reference around which people can communicate, feel comfortable and measure progress toward solutions to problems.