IB3200-无代写
时间:2023-05-31
Module Code: IB3200 Occasion: #1 Academic Year: 2021/22
Module Title: SIMULATION
Module Leader(s): Dr KATHYRN HOAD
General Comments
Comments:
I was generally pleased with the overall level of understanding and exam performance. Students
showed skills in drawing out the important information from the given story and interpreting and
applying it to the questions asked. Below are the exam questions with more specific feedback for
each question.
Question Specific Comments
[Question 1] (62 marks in total)
Please read the following ‘story’ and then answer Questions 1a), b), c) which are
based on this text:
The Arthur Aspel Hospital is a reasonably large hospital which provides primary and specialized
health care services. It has an Emergency Department (ED) which is responsible for triage and
treatment of patients arriving at the hospital. The ED is open 24 hours a day, 7 days a week.
Doctors, nurses and other staff work 8 hour shifts. It is known that arrival rates of patients into ED
changes depending on the time of year, the day of the week, as well as the time of day. The layout of
the ED is shown in Figure 1.1.
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Figure 1.1: Current layout of the Emergency Department at the Arthur Aspel Hospital. Not drawn to
scale, nor is the number of seats shown indicative of the waiting capacity available.
The ED has 16 beds in total, situated in the ICU; 8 are reserved for accident victims and critical care
and 8 are reserved for patients who are acutely ill.
Mobile patients (i.e. patients who get themselves to the hospital ED) enter the ED at entrance A.
They report to reception where their details (name, address, age and main symptoms/issues) are
taken and logged onto the computer system by a receptionist. They are then asked to wait in the
waiting area until called by a triage nurse.
The triage nurse calls the waiting patients into the triage room according to both order of arrival and
recorded severity of symptoms/issues (e.g. anyone displaying possible stroke symptoms will be seen
as a priority regardless of when they arrived). The triage nurse assesses the patient for critical
symptoms (high blood pressure, fever, etc.) and assigns a triage code to the patient depending on
their condition (1 to 5, 1 being the most critical). If the patient is deemed to be in critical condition
(code 1) they are transferred to the ICU room for immediate care. Otherwise, the patient is asked to
return to the waiting room to wait to be called for further assessment in one of the examination
rooms by a doctor.
How long a mobile patient waits depends on the availability of doctors, examination rooms and the
triage code (priority) assigned to the patient. Triage codes assign a priority to a patient based on the
patient’s condition. Waiting time targets are associated with each code. Patients assigned code 1
should have no waiting time (critical condition). Patients with codes 2, 3, 4 and 5 should not wait
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more than 15, 30, 60 and 120 minutes respectively from being registered at reception to having their
1st assessment (exam 1) by a doctor in an examination room.
After a patient is first assessed (exam 1) by a doctor in an examination room, the doctor might
require lab tests to be performed (e.g. blood tests, X-ray, etc.). If tests are not required, the patient
is either discharged to go home or transferred to another department for admission into the
hospital. If tests are required, any tests that can be taken within the examination room such as blood
tests are carried out, or the patient is taken to another part of the hospital for the tests (e.g. scans) to
be carried out. The patient then returns to the waiting room to await the results of the tests and be
called to a 2nd assessment (exam 2) by the doctor. After the 2nd assessment (exam 2) the patient is
either discharged to go home or transferred to another department for admission to the hospital.
After completion of the first examination (exam 1), the target is that all mobile patients should not
have to wait longer than 3 hours before being either discharged home or transferred to another
department for admission.
Patients arriving by ambulance are taken directly to the ICU room for assessment and treatment
without visiting the waiting room, triage room or examination rooms.
In the examination rooms, doctors and nurses work together, so when a doctor is assigned to a
patient, a nurse is also assigned. Likewise, when a doctor finishes with a patient and becomes free,
so does a nurse. On any shift there are 5 doctors and 5 nurses that work in the examination rooms, 1
doctor and 3 nurses that work only in the ICU room, 1 triage nurse in the triage room and 2
receptionists. Each triage nurse and receptionist can see one patient at a time. Each pair of doctor
and nurse in the examination rooms can also only see one patient at a time. The other nurses and
doctor in the ICU deal with multiple patients at a time.
The Arthur Aspel ED does not currently meet its waiting time targets for triage codes 2, 3, 4 and 5.
Since these delays affect approximately 92% of patients visiting ED, the hospital has engaged your
consultancy company to investigate how the targets might be achieved.
Your consultancy company decides to build a discrete event simulation of this ED. The main
modelling objective of this DES project is to improve the care process by bringing patient waiting
times for those given triage codes 2, 3, 4, and 5 to their set targets or below. In order to achieve
these targets, the hospital is willing to consider altering the numbers of doctors, nurses and
examination rooms, but wish to achieve a reasonably high utilization of all these resources. The
hospital management are willing to consider increasing number of examination room doctors by a
maximum of 2, examination room nurses by a maximum of 2, triage nurses by a maximum of 2 and
examination rooms by a maximum of 2. The Key Performance Indicators (Outputs) for the model are
agreed to be:
 Waiting times for mobile patients from being registered at reception to starting their first
assessment (exam 1) by a doctor in an examination room.
 Time mobile patients spend in ED after completing first examination (exam 1) to being
discharged home or being transferred to another department for admission (this process
includes lab test processing, waiting for exam 2, exam 2 duration and waiting for transfer).
 Utilization of doctors, nurses and examination rooms.
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The Hospital requires recommendations within 3 months. Your consultancy firm will build and use
the DES model to both provide these recommendations and to create discussion and buy-in from the
various stakeholders involved. Your consultancy firm also wish to be able to re-use parts of this DES
model for future health care modelling projects.
Imagine you are the consultant who is working with the Hospital to investigate the performance of
its ED. You have been commissioned to build a DES model of their system problem (as described
above) and to experiment with this model in order to provide them with recommendations of how
to proceed.
Now answer Questions 1 a, b, c.
a) Draw a process flow diagram for the current ED system that would inform the creation of a
DES model for this system problem. Clearly state and justify any assumptions and/or
simplifications you rely on (if any) in order to draw this diagram.
(25 marks)
Comments:
This was generally tackled well by students. The main error was including the ambulance arrivals
and ICU details in the diagram as these were outside the scope of the problem set. Other common
errors were not including queues (circles) before each activity, or missing off the necessary
resources information. There were also some diagrams where the flow around the system was
unclear with entities theoretically stuck in never ending loops. Strategically placed decision points
were allowed and some students used them to help clarify looping which would otherwise have
been unclear and incorrect. A very few students drew a logic flow diagram instead of the required
process flow diagram.
The following is an example of an appropriate diagram for this question, but other appropriate
configurations were possible and would have gained marks accordingly.
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b) Clearly describe and list what model realization data / information is required for a DES model
of the current ED for this system problem as described.
(12 marks)
Comments:
Where students lost marks on this question was either by simply not writing down enough, or by
incorrectly stating waiting and queuing times as model realization data. What was needed was the
data / information required to make the model mimic the real system, e.g.
- Arrival data for ‘mobile patients’ visiting ED
- Staff shift patterns
- Reception service times
- Triage service times
- Exam 1 service times
- Exam 2 service times
- Lab tests service times
- Transfer to other depts times
- Percentage of patients given the different triage codes (1 to 5)
- Percentage of patients requiring lab tests / or exam 2
- Percentage of patients requiring discharge after exam 1
- Percentage of patients requiring discharge after exam 2
- Percentage of patients requiring transfer to hosp admission after exam 1
- Percentage of patients requiring transfer to hosp admission after exam 2
c) Justify and explain how you would carry out the experimentation for this DES of the described
ED problem. Include the use of an appropriate formal experimentation technique(s) (e.g.
experimental design or optimisation method) in selecting and comparing your scenarios, and
use of appropriate statistical tests, in order to provide recommendations to the Hospital
Management. Make clear the link(s) between your stated scenarios, the model outputs (KPIs)
and model objectives. (Note that you are NOT expected to actually carry out this
experimentation, therefore it is NOT expected that you would be able to state any actual
results or recommendations. But it is expected that you should be able to explain in context
the scenarios you would run, the methods you would use and the decision procedures you
would carry out.)
(25 marks)
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Comments:
Expected to see a full detailed and justified explanation of interactive and possibly non-interactive
experimentation in context. Expected factorial design or complete set of scenarios to be clearly
explained in context. In this case, you really only needed to consider two experimental factors:
Triage nurses, and combined exam rooms/drs/nurses. Some students realized this but most
didn’t. The answer should have considered code targets and you could have discussed other
factors that could be used to decide between scenarios for giving recommendations.
Expected a full detailed and justified explanation of how you would statistically compare scenario
results for your chosen KPIs with a clear and correct explanation of what would be considered a
‘best’ result i.e. min, max, etc..
Expected a clear understanding of links between the scenarios, KPIs and objectives would be
shown in the answer. The answer should have therefore explained clearly the objectives, KPIs, exp
factors/scenarios and they needed to be consistent and logical.
Quite a few students just explained some experimentation but not the objectives, KPIs,… Some
students explained black box validation or output analysis rather than experimentation. Others
explained the 2k experimentation quite well but failed to explain how you could compare the
scenario results.
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[Question 2]
Carry out a manual simulation of the arrival of mobile patients at the ED described in Question 1
using the following information. Assume that an exponential distribution is suitable for modelling
the inter-arrival times of mobile patients between 11am and 1pm on Mondays. Assume that the
mean inter-arrival time was estimated to be 30 seconds. Use the inverse-transformation method to
sample two inter-arrival times from this distribution, using two random numbers chosen from table
2.1, using the instructions given. Assume that the previous mobile patient entered the ED at
11:01:30. Calculate the two times that the next two mobile patients enter the ED using the format
Hour: Minutes: Seconds: HH:MM:SS. Show your workings clearly and round your answers to the
nearest whole second.
[NB. The CDF for the Exponential distribution is () = 1 − ିఒ௫, where represents the sampled
inter-arrival time and ଵ

is the mean inter-arrival time.]
Table 2.1: random numbers
Instructions: Take your student ID number. Use the last two digits as column number and
row number, in that order. Look for the random number that lies in the cell that is in that
column and row. Use that random number and the one that is directly below it. Use them
in that order. For example: If your ID was 1813816, look in column 1, row 6 and therefore
use the random numbers 0.625, 0.31, in that order.
Column
Row
0 1 2 3 4 5 6 7 8 9
0 0.061 0.519 0.158 0.08 0.765 0.537 0.787 0.078 0.659 0.244
1 0.603 0.034 0.605 0.618 0.286 0.088 0.167 0.815 0.117 0.911
2 0.919 0.523 0.16 0.047 0.052 0.765 0.512 0.002 0.724 0.328
3 0.669 0.904 0.864 0.647 0.386 0.015 0.221 0.696 0.305 0.07
4 0.284 0.222 0.632 0.237 0.949 0.685 0.616 0.989 0.109 0.771
5 0.713 0.898 0.433 0.961 0.672 0.429 0.968 0.431 0.44 0.549
6 0.45 0.625 0.975 0.628 0.018 0.779 0.322 0.254 0.796 0.75
7 0.763 0.31 0.257 0.017 0.698 0.275 0.798 0.761 0.952 0.111
8 0.636 0.935 0.498 0.487 0.35 0.933 0.925 0.442 0.788 0.012
9 0.237 0.68 0.32 0.547 0.882 0.362 0.15 0.05 0.132 0.759
0.622 0.441 0.723 0.834 0.41 0.798 0.791 0.812 0.872 0.201
(8 marks)
Comments:
You could have used either = −30ln (1 − ) Or = −30ln ()
Marks were given for each correct interarrival value calculated and for each correct clock time of
arrival. This question was answered very well by most students. There were a few silly calculation
errors but mostly this question was done correctly.
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[Question 3]
A café opens at 10am and closes at 6pm. Management wishes to reduce waiting times for their
customers. A DES model is built to mimic the opening hours of 11.30am to 5.30pm. Within these
hours the arrival rate of customers vary and the model is built with time dependent arrival
distributions to accommodate this. The modeler has now reached the stage of carrying out Output
Analysis within experimentation validation. She runs it for 10 replications and the output “number of
customers waiting to be served” is collected from the model every 10 minutes. Figure 2.1 shows the
data averaged over the 10 replications plotted on an appropriate graph. Explain in detail how you
would recommend the modeler to proceed given the information given in this question and shown in
Figure 2.1, justifying your recommendations.
Figure 2.1: Output data averaged over 10 replications for output “number of customers waiting to
be served”.
(8 marks)
Comments:
It was expected that students would realize that this type of data collection from the model is used
for checking initialization bias and would realize from the information given that there appears to
be initialization bias in the output, from both the graph and the fact that the café opens 1.5 hours
before simulation starts. It was also expected that students would discuss the type of system and
simulation model i.e. terminating, and the type of output, i.e. transient, in explaining the best way
forward for the modeler. It was hoped that students would recommend observing initial
conditions in the real system and inputting these into the model at start-up to create a more
realistic starting condition. Some students suggested simply running the model from the true start
time (i.e. opening time) of the system so initial bias does not occur which also gained marks if
sufficiently argued and explained. Note that you cannot use MSER-5 / warm-up period here as it is
not steady state output.
Some students answered this question extremely well, but many did not. Some completely missed
that this was asking about initialization bias. Others who did realize this, incorrectly suggested
using MSER-5.
0
2
4
6
8
10
12
0 50 100 150 200 250 300 350
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Time (minutes)
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[Question 4] (22 marks in total)
For the café DES described in Question 3, six different scenarios are run for 50 replications and
compared in an all pairwise fashion. Figure 4.1 shows a selection of the output from the excel file used
to carry out a full pairwise comparison of the six scenarios using the output, KPI: ‘Percentage of
customers waiting more than 3 minutes to be served’.
Figure 4.1: A selection of the output from the excel file used to carry out a full pairwise comparison of
the four scenarios using the output KPI: ‘Percentage of customers waiting more than 3 minutes to be
served’.
a) Using the results in Figure 4.1, clearly state the order of the scenarios from smallest average
KPI to largest. Explain in context, which scenario(s) give the ‘best’ results. Then explain what
other information you would want in order to be able to make a more informed
recommendation to the café management.
(12 marks)
Comments:
The correct order of scenarios for this case is S5 > S1 > S2 = S3 > S4 = S6
It was expected that an answer would explain what is considered ‘best’ in this context, i.e. that you
would want to minimise this type of KPI (% of customers waiting more than 3 minutes), and thus
explain which two scenarios (S4 and S6) have significantly smaller values than other scenarios. Most
students did this correctly but some failed to explain clearly that they were not statistically
significantly different to each other.
………………………………………………………………………………………………………………………..
There were various options for what you might want to see in order to make a more informed
recommendation. But the obvious ones were the ones that most students overlooked, i.e.
what percentage target management want for %? The mean values of KPI for each scenario
+ CIs. More students thought to consider the utilization of resources and costs of implementing the
scenarios.
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b) The comparison of these six scenarios was carried out as a full pairwise comparison with an
overall significance of 10%. What is the Bonferroni corrected significance and confidence for
each individual comparison? Hence comment on the appropriateness of this full pairwise
comparison and suggest how to proceed. Clearly show your calculations and reasoning.
(10 marks)
Comments:
Many students failed to notice that if there are 6 scenarios, then a full pairwise comparison would
entail making 15 comparisons. Therefore the following calculations were then incorrect.
6 scenarios -> 15 comparisons and overall sig of 10% -> 10/15, so significance = 0.6667%
and confidence = 100-0.6667 % = 99.333%
Some students correctly realized that these are very wide CIs which is not desirable. There were
various suggestions that could be made about how to proceed. The option most students suggested
was to lower the overall significance of the tests, but other correct suggestions also gained marks.


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