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risk management exam

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Page1 of 16

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)

Page 2 of 16

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

https://www.ucl.ac.uk/academic-manual/chapters/chapter-4-assessment-framework-taught-programmes/section-3-module-assessment#3.13

Page 3 of 16

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.

https://www.ucl.ac.uk/academic-manual/chapters/chapter-6-student-casework-framework/section-9-student-academic-misconduct-procedure#9.2

Page 4 of 16

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).

https://wiki.ucl.ac.uk/display/ELearningStudentSupport/Moodle+Online+Exams+%2824hrs%29%3A+Handwritten+responses+-+using+Office+Len

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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

https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fsway.office.com%2FVUTG4ObfJjDRbLu1%3Fref%3DLink&data=02%7C01%7C%7C52c8f8cc6dd542d8fb9c08d7e82547f0%7C1faf88fea9984c5b93c9210a11d9a5c2%7C0%7C0%7C637233119123260858&sdata=WQbHDQxlnGQPeEyQlDmCQxk4xi5%2BI580AO7TT%2Bqw5NI%3D&reserved=0

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https://www.ucl.ac.uk/students/student-support-and-wellbeing

Page 6 of 16

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!

Page 7 of 16

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]

Page 8 of 16

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.

E
x

ct
e

a
lu

e
o

f
P

e
rf

e
ct

fo
rm

a
ti

o
n

(
£

K
)

Probability that vaccine is not approved

Page 9 of 16

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 𝑝 MWh

of electricity per year, where 𝑝 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 𝑑 will be 210,000
MWh. With probability 75%, only half their employees will be back in the office, and the electricity

consumption 𝑑 will be 140,000 MWh.

If DataAnalytics’ electricity demand 𝑑 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 𝑑 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 𝑠/MWh.

Page 10 of 16

Expert projections suggest that 𝑠 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

Page 11 of 16

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

Page 12 of 16

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]

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

Page 13 of 16

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

Page 14 of 16

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

Page 15 of 16

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.

Page 16 of 16

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/migrated-
files/UCL_Assessment_Criteria_Guide

Section E: Groupwork Instructions

• Not applicable as this is an individual assessment

Section F: Additional information from module leader(s)

None

https://www.ucl.ac.uk/library/docs/guides/references-plagiarism

https://www.ucl.ac.uk/teaching-learning/sites/teaching-learning/files/migrated-files/UCL_Assessment_Criteria_Guide

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