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Assessment Information for Exam/Test in 24-hour
timed window
Module name: Decision & Risk Analysis
Module code: MSIN0159
Module leader name(s): Kenan Arifoglu (Groups 1, 2), Siddharth Singh (Groups 3, 4), Steve Yoo
(Group 5)
Academic year: 2020-2021
Term 1, 2 or 3: Term 2
Type of assessment: 24-hour timed Online Exam/Test
Nature of assessment – individual or group: Individual
Content of this Assessment Brief
Section Content
A Core information
B Requirements
C Module learning outcomes covered in this
assessment
D Assessment criteria
E Groupwork instructions (if applicable)
F Additional information from module leader (if
applicable)
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Section A: Core information
This assessment is
marked out of:
100 marks
% weighting of this
assessment within total
module mark
70%
Time allowed for
completion of this
assessment
• This assessment should take approximately 3 hour(s) to
complete. You may take longer to complete it if you wish to.
• You have a window of 24 hours from release to submission to
complete it.
• In addition to answering/responding to the
questions/requirements, this 24-hour period provides
enough time for you to prepare your document for
submission (including, as appropriate, copying, pasting,
saving electronically) and loading to Moodle.
• If you have a SORA which allows for additional writing time
for examinations/tests, this has been factored into the 24-
hour window and no additional time in addition to the 24-
hour period is available.
Word count/number of
pages – maximum
No specified limit
Determining word count
impacted by Turnitin
• After submission to Turnitin, the Turnitin recorded word
count is usually higher than the word count in a Word
document.
• Where the assessment brief specifies a maximum word
count, on the front cover of your submission record the
number of words as recorded in your Word document.
• It is the Word document word count which will be taken
account of in marking, NOT the Turnitin word count.
Footnotes, appendices,
tables, figures, diagrams,
charts included
in/excluded from word
count/page length?
Not applicable
Bibliographies, reference
lists included
in/excluded from word
count?
Not applicable
Penalty for exceeding
specified word
count/page length?
• Where there is a specified word count/page length and this is
exceeded, yes there is a penalty: 10 percentage points
deduction, capped at 40% for Levels 4,5, 6, and 50% for Level
7. Refer to Academic Manual Section 3: Module Assessment –
3.13 Word Counts.
• Where there is no specified word count/page length no
penalty applies.
Requirements for/use of
references
• This assessment is an ‘open book’ exam/test which you
attempt at home, at UCL, or indeed in any other location. It is
not invigilated. In principle it should take no longer than the
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time specified above to complete. However, you have a 24-
hour timed window in which to download the assessment, to
complete it, and to submit it to Moodle.
• In responding to the demands of this assessment, you may
draw upon course materials – lecture slides, notes, handouts,
readings, textbook(s) – you engaged with in your studying of
this module.
• You are not expected or required to find and use new
materials. In a formal ‘sit-down’ invigilated exam/test you
would not be able to find and draw upon new materials – you
would draw upon what you learned from your studying of the
module.
• You may refer to such course materials but you should not be
copying word for word from lecture slides, notes, handouts,
readings, textbook(s) you engaged with in your studying of
this module.
• You should capture, articulate and communicate your views,
thoughts and learning in your own words.
• If you do provide quotes from any lecture slides, notes,
handouts, readings, textbook(s) you should cite them and
provide references in the usual way.
• Be aware that a number of academic misconduct checks,
including the use of Turnitin, are available to your module
leader.
• If required/where appropriate UCL Academic Misconduct
penalties may be applied (see immediately below).
Academic misconduct
(including plagiarism)
• Academic integrity is paramount.
• It is expected that your submission and content will be your
own work with no academic misconduct.
• Academic Misconduct is defined as any action or attempted
action, including collusion with other students, that may
result in a student obtaining an unfair academic
advantage. There are severe penalties for Academic
Misconduct, including, where appropriate and required,
exclusion from UCL.
• Refer to Academic Manual Section 9: Student Academic
Misconduct Procedure – 9.2 Definitions.
Submission date 23rd March, 2021
Submission time 10:00 am GMT
Penalty for late
submission?
Late submissions are not permitted
Submitting your
assignment
The assignment MUST be submitted to the module submission link
located within this module’s Moodle ‘Assessment’ section by the
specified deadline.
Anonymity of identity.
Normally, all submissions
are anonymous unless
the nature of the
• Anonymity is required.
• Your name should NOT appear anywhere on your submission.
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submission is such that
anonymity is not
appropriate, illustratively
as in presentations or
where minutes of group
meetings are required as
part of a group work
submission
Return and status of
marked assignments
• At the latest this will be within 4 weeks from the date
of submission as per UCL guidelines, but we will
endeavour to return it earlier than this.
• Assessments are subject to appropriate double
marking/scrutiny, and internal quality inspection by
a nominated School of Management internal
assessor. All results when first published are
provisional until confirmed by the relevant External
Examiner and the Examination Board.
• No appeals regarding your published mark are
available until after confirmation by that
Examination Board. UCL regulations specify that
academic judgment applied within the marking
process cannot be challenged.
Academic Support with this Assessment
Given the nature of this assessment, during the 24-hour window no questions should be directed to
the Module Leader/Module Team. If you have doubts about wording or requirements etc., state your
assumptions. If they are appropriate they will be taken into consideration in marking.
Uploading your submission
• Unless specifically instructed otherwise in the assessment document, please upload your
work as a single file via the submission link on Moodle.
o Wherever possible you should type/use Excel for (as appropriate) your answers and
follow instructions later in this assessment document.
o If you do have to include any elements that are not typed/computer generated (e.g.
figures, diagrams, equations etc.), or you are unable to type your answers for any
reason, please follow the advice for submitting handwritten answers for any
submission that requires scanning documents (the webpage refers to 24-hour timed
exams but is applicable to all online submissions including this one).
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o If for any reason you are not able to use the app recommended by ISD at the link
above, you can consult the following resources for advice about preparing your
submission:
▪ Submitting handwritten assignments to Moodle using mobile or tablet Devices
– Device Camera
▪ Submitting handwritten assignments to Moodle using mobile or tablet devices
– MS One Drive App
• Please DOUBLE CHECK that the file you are uploading is the correct one and is complete
(with all pages visible).Resubmission will not be permitted.
Technical Problems
If you encounter difficulties downloading or submitting your assessment via Moodle, then please
immediately notify (by email) your department (Programme Administrators ONLY), explaining the
problem and including a copy of the work you are trying to submit. ONLY use this approach if you
can show that you have tried to download from/upload to Moodle and encountered technical
difficulties.
Advice and other support
• Student Support and Wellbeing
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Section B: Requirements
There are THREE (3) sections to the examination paper. All three sections are independent of each
other.
Section A consists of FOUR (4) questions. This section is worth FORTY (40) marks.
Section B consists of FOUR (4) questions. This section is worth FORTY (40) marks.
Section C consists of TWO (2) questions. This section is worth TWENTY (20) marks.
Good luck!
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SECTION A
mRNATech is a large pharmaceutical firm that is working on a new vaccine against Covid 19. The
vaccine needs to be approved before it can actually be used to vaccinate people. The vaccine
development and approval process will take six months. To ensure that the vaccine is readily available
after the approval, mRNATech needs to invest one million GBP (£1,000K) in its capacity. If the vaccine
is approved, mRNATech expects to make 6% return on investment, i.e., the net profit after subtracting
the initial capacity investment is equal to sixty thousand GBP (£60K).
However, there is a 5% chance that the vaccine is not effective enough so that it will not be approved
by the government. If the vaccine is not approved, mRNATech can salvage its capacity to another
vaccine manufacturer for £500K. mRNATech has to decide whether or not to invest in the capacity
now. If it decides not to make the investment and cease the project now, it can use £1,000K to make
an alternative investment that will return £10K sure net profit.
Question 1: Evaluation of the Capacity Investment
a) Construct the decision tree for mRNATech’s decision problem. Assuming it is risk-neutral,
would you recommend mRNATech to make the capacity investment?
[6 marks]
b) Define the risk profiles associated with the optimal strategy. Taking risk into
consideration, what would be your recommendation to mRNATech? While determining your
recommendation, assume that mRNATech is a large pharmaceutical firm that considers
investing in around 1000 similar projects every year.
[4 marks]
Question 2: Value of Perfect Information
mRNATech is considering hiring DataAnalytics, an independent third party company, which would be
able to predict whether mRNATech’s vaccine will be approved or not
Suppose DataAnalytics is able to predict whether the vaccine will be approved or not with
perfect accuracy. What is the maximum that mRNATech should be willing to pay in order to
obtain this perfect information? Answer this question by constructing a decision tree.
[10 marks]
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Q3: Sensitivity Analysis
Figure 1 below shows the value of the perfect information as a function of the probability that
mRNATech’s vaccine fails.
Figure 1: The value of the perfect information provided by DataAnalytics against the
probability that mRNATech’s vaccine is not approved
Can you explain the shape of Figure 1? In particular i) why is the value zero when the
probability that the vaccine is not approved is 0%, ii) why does it increase from 0% to 9% and
then iii) why does it decrease for values greater than 9%? iv) When is information most
valuable?
[10 marks]
Question 4: Value of Imperfect Information
DataAnalytics charges mRNATech £15K for predicting whether the vaccine will be approved or not.
For this fee, it will conduct a detailed analysis of the vaccine and provide a recommendation to
mRNATech, either “favourable” or “unfavourable”. The probability that DataAnalytics will make a
favourable recommendation is equal to 91.75%.
Unfortunately, DataAnalytics’s recommendations can sometimes be wrong. The probability that the
vaccine will not be approved given a favourable recommendation by DataAnalytics is 1.63%. On the
other hand, the probability that the vaccine will not be approved given an unfavourable
recommendation by DataAnalytics is 42.42%.
£-
£5
£10
£15
£20
£25
£30
£35
£40
0.0% 10.0% 20.0% 30.0% 40.0% 50.0%
Expected Value of Perfect
Information (£K)
Probability that vaccine is not approved
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Given these statistics, mRNATech is wondering whether it would be worthwhile to pay £15K to
DataAnalytics to perform this analysis.
a) What is the value of imperfect information that DataAnalytics provides? Should mRNATech
hire DataAnalytics? Construct a decision tree to answer this question.
[7 marks]
b) Ignoring the cost of hiring DataAnalytics, define the risk profiles for the case when
mRNATech hires DataAnalytics. Taking into account the risk, would you recommend
mRNATech to pay £15K to hire DataAnalytics?
[3 marks]
SECTION B
In line with their corporate responsibility targets, DataAnalytics, an analytics firm, has committed to
satisfy 100% of its electricity demand using clean energy in the year 2022. They are currently in the
process of planning how to achieve this target.
In order to hedge against possible variations in the price of electricity in 2022, DataAnalytics plans to
contract solar capacity from SolarNow, a nearby solar farm, through a Corporate Power Purchase
Agreement (CPPA). SolarNow has offered two possible CPPA contracts:
• Contract A: 100 MW of capacity; DataAnalytics must purchase all the output of its contracted
100 MW of solar capacity at a price of £50/MWh.
• Contract B: 150 MW of capacity; DataAnalytics must purchase all the output of its contracted
150 MW of solar capacity at a price of £40/MWh.
However, because of variations in weather, the amount of electricity output that SolarNow’s solar
panels will produce is uncertain. In particular, every MW of capacity is projected to produce MWh
of electricity per year, where has a mean of 1500 MWh and a standard deviation of 120 MWh. The
distribution is symmetric around its mean.
Given the current work-from-home arrangements under which DataAnalytics is operating, it is unclear
how many employees will be working from home versus in the offices in 2022. With probability 25%,
all their employees will be back in the office and the firm’s 2022 electricity demand will be 210,000
MWh. With probability 75%, only half their employees will be back in the office, and the electricity
consumption will be 140,000 MWh.
If DataAnalytics’ electricity demand falls short of the amount of electricity delivered by the contract,
they must still honour the terms of the contract and pay SolarNow the entire amount, as per the
contract terms. However, if exceeds the amount of electricity delivered by the contract, they must
make up the shortfall by purchasing wind or solar energy from the spot market at a price /MWh.
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Expert projections suggest that will be somewhere between £30/MWh and £70/MWh, with equal
probability.
DataAnalytics is seeking your help to understand which of the contracts to choose, based on the total
cost to associated with each contract.
Question 5: Problem Setup and Scenario Analysis
a) For each of the contracts, write an expression for DataAnalytics’ total cost in terms of the
uncertain production, demand and spot price.
[5 marks]
b) If you were to take a decision to minimize the probability that DataAnalytics must
purchase from the spot market, which contract would you choose and why?
[2 marks]
c) If you were to take a decision simply based on the expected value of the parameters,
which contract would you choose?
[5 marks]
Question 6: Choice of Distributions for Simulation
a) What distributions should be used to model each of the uncertain parameters?
[4 marks]
b) Will the total cost have a discrete or a continuous distribution? Why?
[3 marks]
Question 7: Interpreting the Simulation Output
You decide to simulate the performance of both contracts using a 10000-iteration simulation. After
performing the simulation, you obtain summary statistics of the resulting output distributions (Tables
1 and 2), and plot the associated cumulative distribution functions of the output distributions (Figure
2).
Summary Statistics
Contract A Contract B
Mean £8,292,719 £9,006,185
St. Dev £1,391,999 £685,399
Table 1: Summary statistics of the output from the simulation
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Cumulative Distribution of Total Cost
Contract A Contract B
0.0% £6,434,238 £5,909,147
0.5% £6,807,344 £7,181,025
1.0% £6,861,018 £7,393,249
2.5% £6,927,454 £7,655,098
5.0% £6,973,858 £7,902,607
10.0% £7,010,445 £8,181,205
15.0% £7,061,124 £8,360,084
20.0% £7,139,003 £8,442,475
25.0% £7,233,177 £8,536,878
30.0% £7,332,629 £8,622,942
35.0% £7,438,955 £8,712,966
40.0% £7,538,802 £8,806,180
45.0% £7,637,415 £8,899,689
50.0% £7,742,085 £8,986,699
55.0% £7,856,388 £9,077,417
60.0% £7,988,681 £9,164,362
65.0% £8,149,006 £9,255,924
70.0% £8,376,985 £9,358,809
75.0% £9,157,284 £9,464,706
80.0% £9,816,263 £9,587,282
85.0% £10,269,846 £9,721,398
90.0% £10,737,336 £9,896,266
95.0% £11,197,635 £10,151,662
97.5% £11,444,343 £10,387,113
99.0% £11,645,447 £10,643,191
99.5% £11,756,747 £10,832,431
100.0% £12,187,547 £11,609,436
Table 2: Cumulative Distribution of Total Cost for Each Contract
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Figure 2: Comparison of Cumulative Distribution Functions for cost associated with Contract A and
Contract B
a) What are the realistic maximum and minimum costs associated with each of the contracts?
[4 marks]
b) Which contract is associated with a higher probability of a cost less than £8 million? Which
contract is associated with a higher probability of a cost greater than £11 million?
[2 marks]
c) If your decision was based on minimizing the expected value of the cost, which contract
would you choose? Does this agree with your assessment in Q5c, and if not, why not?
[5 marks]
d) Does any one of the contracts dominate the other? Explain.
[3 marks]
0%
20%
40%
60%
80%
100%
£6,500,000 £7,500,000 £8,500,000 £9,500,000 £10,500,000 £11,500,000
Cost — Contract A Cost — Contract B
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Question 8: Sensitivity Analysis
Shown in Figure 3 are tornado diagrams associated with each of the contracts
Figure 3: Tornado Diagrams for Contract A and Contract B
a) What do each of these tornado diagrams tell you?
[5 marks]
b) If DataAnalytics were to go ahead with Contract A, what measures would you recommend
to reduce the effect of uncertainty on the output?
[2 marks]
SECTION C
mRNATech also manufactures three other antiviral drugs against Covid-19, namely, drugs A, B and
C. The antiviral drugs are produced by blending two chemicals: chemical 1 and 2. In order to ensure
the desired effect against the virus, drug A must contain at least 60% chemical 1, drug B must contain
at least 50% chemical 1, and drug C must contain at least 35% chemical 1. Drug A sells for £6 per
oz, drug B sells for £4 per oz, and drug C sells for £5 per oz.
Both chemicals can be produced using either of two production processes, both of which use the
same kind of raw material, and require skilled labour. When process 1 is run for an hour, it requires 4
oz of raw material and 1.5 hours labour, and it yields 3 oz of each chemical. When process 2 is run
for an hour, it requires 2 oz of raw material and 2 hours of skilled labour and yields 2 oz of chemical
1 and 1 oz of chemical 2. mRNATech has a total of 120 hours of skilled labour and 100 oz of raw
material.
0.0000 0.5000 1.0000
s
p
d
Cost — Contract A
Correlation Coefficients
0.0000 0.5000 1.0000
s
d
p
Cost — Contract B
Correlation Coefficients
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mRNATech wants to understand how best to use the chemicals and processes available to it to
manufacture the three drugs.
Question 9. Optimization Model
Construct an optimization model that can be used to solve mRNATech’s decision problem
above. In particular, what are the decision variables? In terms of the decision variables, list
the objective and constraints formally.
[10 marks]
Question 10. Sensitivity Analysis
The sensitivity Report generated by Excel Solver for the above model is illustrated by Figure 4.
Figure 4: Sensitivity report generated by Excel Solver for mRNATech’s optimization problem (only
sensitivity report related with the constraints are provided)
a) The production manager at mRNATech notes that they can get additional skilled labour
hours up to 50 hours at £1 per hour. How many hours of skilled labour should mRNATech
get? Clearly state your reasoning.
[5 marks]
b) The supplier offers mRNATech 50 oz of additional raw material at £8 per oz. Should
mRNATech accept the offer? Clearly explain your reasoning.
[5 marks]
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$C$4 Minimum requirement for drug A 90 -3.55271E-15 0 10 15
$D$4 Minimum requirement for drug B 0 – 4 0 12.5 0
$E$4 Minimum requirement for drug C 0 -1.538461538 0 16.25 0
$G$10 Total Chemical 1 Required 90 6 0 37.5 25
$G$11 Total Chemical 2 Required 60 6 0 16.66666667 25
$G$4 Total Labour Hours Required 75 0 120 1E+30 45
$G$7 Total Raw Material Required 100 9 100 60 100
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Section C: Module Learning Outcomes covered in this
Assessment
This assignment contributes towards the achievement of the following stated module
Learning Outcomes as below:
By the end of this course you will be equipped with specific skills in the areas of data analysis,
structuring decisions, building decision models, risk assessment, and decision making under
uncertainty, recognising areas where business analysis can add value, selecting appropriate
types of analyses and applying them in a small-scale, quick-turnaround fashion.
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Section D: Assessment criteria
Within each section of this coursework you may be assessed on the following aspects, as
applicable and appropriate to this particular assessment, and should thus consider these aspects
when fulfilling the requirements of each section:
• The accuracy of any calculations;
• The strengths and quality of your overall analysis and evaluation;
• Appropriate use of relevant theoretical models, concepts and frameworks;
• The rationale and evidence that you provide in support of your arguments;
• The credibility and viability of the evidenced conclusions/recommendations/plans of
action you put forward;
• Structure and coherence of your considerations and reports;
• As and where required, relevant and appropriate, any references should use either
the Harvard OR Vancouver referencing system (see References, Citations and
Avoiding Plagiarism)
• Academic judgement regarding the blend of scope, thrust and communication of
ideas, contentions, evidence, knowledge, arguments, conclusions.
• Each part has requirements with allocated marks, maximum word count limits/page
limits and where applicable, templates that are required to be used.
You are advised to refer to the UCL Assessment Criteria Guidelines, located at
https://www.ucl.ac.uk/teaching-learning/sites/teaching-learning/files/migratedfiles/UCL_Assessment_Criteria_Guide.pdf
Section E: Groupwork Instructions
• Not applicable as this is an individual assessment
Section F: Additional information from module leader(s)
None

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