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IB3200-无代写
时间：2023-05-31
UNIVERSITY OF WARWICK
Department Warwick Business School
Level 3
Module Code IB3200
Module Title Simulation
Exam Paper Code IB3200_C
Exam Paper Title IB3200_Simulation _Exam Paper [Summer]
2021-2022
Duration 2 hours
Exam Paper Type Fixed time – Open Book
STUDENT INSTRUCTIONS
1. Read all instructions carefully. We recommend you read through the entire paper at
least once before writing.
2. There are FOUR questions. All candidates should attempt every question.
3. You should not submit answers to more than the required number of questions.
4. The number of marks available is indicated at the start of each question.
5. Where handwritten answers are permitted, please ensure you write legibly, preferably
in dark blue or black ink. If you use a pencil, please ensure it is not too faint to be
captured by scan or photograph. It is your responsibility to ensure your work can be
read.
6. If uploading photographs or scanned copies of your work, please check for legibility
before uploading. It is your responsibility to ensure your work can be read.
7. Add your student number to all uploaded files.
8. You are permitted to access module materials, notes, resources, references and the
internet during the online assessment.
9. You must not communicate with any other candidate during the assessment period,
unless instructed to do so as part of the assessment requirement(s).
IB3200_C
Page 2 of 10
IB3200_C
10. By starting this assessment, you are declaring yourself fit to undertake it. You are
expected to make a reasonable attempt at the assessment by answering the questions
in the paper.
IMPORTANT INFORMATION
• We strongly recommend you use Google Chrome or Mozilla Firefox to access the
Alternative Exams Portal.
• You must have completed and uploaded the assessment within the period of time
provided.
• You are granted an additional 45 minutes beyond the stated duration (2 hours) of this
assessment to allow for downloading/uploading your assessment, your files and any
technical delays.
• Late submissions are not accepted. Once started, you must complete the assessment
within 2 hours (+45 minutes upload/download time).
• If you are unable to submit your assessment, you can record Mitigating Circumstances
and the Board of Examiners will consider your case.
• Students with approved Alternative Exam Arrangements (Reasonable Adjustments) that
permit extra time and/or rest breaks will have this time added on to the stated duration.
SUPPORT DURING THE ASSESSMENT
Operational Support
• Use the Alternative Exams Portal to seek advice immediately if during the
assessment period:
o you cannot access the online assessment
o you believe you have been given access to the wrong online assessment
Operational support will be available between 09:00 and 17:00 UK Time for each
examination (excluding Sunday)
Technical Support
• If you experience any technical difficulties with the Alternative Exam Portal please
contact helpdesk@warwick.ac.uk
Page 3 of 10
IB3200_C
• If you experience technical difficulties with Moodle please contact
moodle@warwick.ac.uk
• If you experience technical difficulties with Questionmark Perception (QMP) please
contact eassessment@warwick.ac.uk
• If you experience technical difficulties with myWBS, please contact
exams@wbs.ac.uk
Technical support will be available between 09:00 and 17:00 UK Time for each
examination (excluding Sunday)
Academic Support
• If you have an academic query, contact the invigilator (using the ‘Contact an
Invigilator’ tool in AEP) to raise your issue. Please be aware that two-way
communication in AEP is not currently possible
Academic support will normally be provided for the duration of the online
examination (i.e. for a 2 hour (+45 min) exam starting at 09:30 UK Time, academic
support would normally be provided between 09:30 and 12:15 UK Time). Academic
support beyond this time is at the discretion of the department
Other Support
• Write to your department immediately if you cannot complete your assessment
for the following reasons:
o you lose your internet connection
o your device fails
o you become unwell and are unable to continue
o you are affected by circumstances beyond your control
Your assessment starts below.
Page 4 of 10
IB3200_C
[Question 1] (62 marks in total)
Please read the following ‘story’ and then answer Questions 1a), b) and c) which are
based on this text:
The Arthur Aspel Hospital is a reasonably large hospital which provides primary and specialised
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.
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.
(Question 1 continues on the next page)
Page 5 of 10
IB3200_C
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
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.
(Question 1 continues on the next page)
Page 6 of 10
IB3200_C
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 utilisation of all these resources. The
hospital management are willing to consider increasing the 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).
• Utilisation of doctors, nurses and examination rooms.
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 and c.
(Question 1 continues on the next page)
Page 7 of 10
IB3200_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)
b) Clearly describe and list what model realisation data / information is required for a DES model
of the current ED for this system problem as described.
(12 marks)
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)
(Continued…/)
Page 8 of 10
IB3200_C
[Question 2] (8 marks in total)
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 − −, where represents the sampled
inter-arrival time and
1
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)
(Continued…/)
Page 9 of 10
IB3200_C
[Question 3] (8 marks in total)
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 3.1 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 provided in this question and
shown in Figure 3.1, justifying your recommendations.
Figure 3.1: Output data averaged over 10 replications for output “number of customers waiting to
be served”.
(8 marks)
(Continued…/)
0
2
4
6
8
10
12
0 50 100 150 200 250 300 350
N
u
m
b
er
o
f
cu
st
o
m
er
s
w
ai
ti
n
g
to
b
e
se
rv
ed
.
Time (minutes)
Page 10 of 10
IB3200_C
[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 six 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, justifying your
argument. 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)
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 therefore suggest how to proceed. Clearly show your calculations and
reasoning.
Department Warwick Business School
Level 3
Module Code IB3200
Module Title Simulation
Exam Paper Code IB3200_C
Exam Paper Title IB3200_Simulation _Exam Paper [Summer]
2021-2022
Duration 2 hours
Exam Paper Type Fixed time – Open Book
STUDENT INSTRUCTIONS
1. Read all instructions carefully. We recommend you read through the entire paper at
least once before writing.
2. There are FOUR questions. All candidates should attempt every question.
3. You should not submit answers to more than the required number of questions.
4. The number of marks available is indicated at the start of each question.
5. Where handwritten answers are permitted, please ensure you write legibly, preferably
in dark blue or black ink. If you use a pencil, please ensure it is not too faint to be
captured by scan or photograph. It is your responsibility to ensure your work can be
read.
6. If uploading photographs or scanned copies of your work, please check for legibility
before uploading. It is your responsibility to ensure your work can be read.
7. Add your student number to all uploaded files.
8. You are permitted to access module materials, notes, resources, references and the
internet during the online assessment.
9. You must not communicate with any other candidate during the assessment period,
unless instructed to do so as part of the assessment requirement(s).
IB3200_C
Page 2 of 10
IB3200_C
10. By starting this assessment, you are declaring yourself fit to undertake it. You are
expected to make a reasonable attempt at the assessment by answering the questions
in the paper.
IMPORTANT INFORMATION
• We strongly recommend you use Google Chrome or Mozilla Firefox to access the
Alternative Exams Portal.
• You must have completed and uploaded the assessment within the period of time
provided.
• You are granted an additional 45 minutes beyond the stated duration (2 hours) of this
assessment to allow for downloading/uploading your assessment, your files and any
technical delays.
• Late submissions are not accepted. Once started, you must complete the assessment
within 2 hours (+45 minutes upload/download time).
• If you are unable to submit your assessment, you can record Mitigating Circumstances
and the Board of Examiners will consider your case.
• Students with approved Alternative Exam Arrangements (Reasonable Adjustments) that
permit extra time and/or rest breaks will have this time added on to the stated duration.
SUPPORT DURING THE ASSESSMENT
Operational Support
• Use the Alternative Exams Portal to seek advice immediately if during the
assessment period:
o you cannot access the online assessment
o you believe you have been given access to the wrong online assessment
Operational support will be available between 09:00 and 17:00 UK Time for each
examination (excluding Sunday)
Technical Support
• If you experience any technical difficulties with the Alternative Exam Portal please
contact helpdesk@warwick.ac.uk
Page 3 of 10
IB3200_C
• If you experience technical difficulties with Moodle please contact
moodle@warwick.ac.uk
• If you experience technical difficulties with Questionmark Perception (QMP) please
contact eassessment@warwick.ac.uk
• If you experience technical difficulties with myWBS, please contact
exams@wbs.ac.uk
Technical support will be available between 09:00 and 17:00 UK Time for each
examination (excluding Sunday)
Academic Support
• If you have an academic query, contact the invigilator (using the ‘Contact an
Invigilator’ tool in AEP) to raise your issue. Please be aware that two-way
communication in AEP is not currently possible
Academic support will normally be provided for the duration of the online
examination (i.e. for a 2 hour (+45 min) exam starting at 09:30 UK Time, academic
support would normally be provided between 09:30 and 12:15 UK Time). Academic
support beyond this time is at the discretion of the department
Other Support
• Write to your department immediately if you cannot complete your assessment
for the following reasons:
o you lose your internet connection
o your device fails
o you become unwell and are unable to continue
o you are affected by circumstances beyond your control
Your assessment starts below.
Page 4 of 10
IB3200_C
[Question 1] (62 marks in total)
Please read the following ‘story’ and then answer Questions 1a), b) and c) which are
based on this text:
The Arthur Aspel Hospital is a reasonably large hospital which provides primary and specialised
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.
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.
(Question 1 continues on the next page)
Page 5 of 10
IB3200_C
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
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.
(Question 1 continues on the next page)
Page 6 of 10
IB3200_C
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 utilisation of all these resources. The
hospital management are willing to consider increasing the 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).
• Utilisation of doctors, nurses and examination rooms.
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 and c.
(Question 1 continues on the next page)
Page 7 of 10
IB3200_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)
b) Clearly describe and list what model realisation data / information is required for a DES model
of the current ED for this system problem as described.
(12 marks)
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)
(Continued…/)
Page 8 of 10
IB3200_C
[Question 2] (8 marks in total)
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 − −, where represents the sampled
inter-arrival time and
1
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)
(Continued…/)
Page 9 of 10
IB3200_C
[Question 3] (8 marks in total)
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 3.1 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 provided in this question and
shown in Figure 3.1, justifying your recommendations.
Figure 3.1: Output data averaged over 10 replications for output “number of customers waiting to
be served”.
(8 marks)
(Continued…/)
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Page 10 of 10
IB3200_C
[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 six 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, justifying your
argument. 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)
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 therefore suggest how to proceed. Clearly show your calculations and
reasoning.
