MANM304/7/SEMR2/21/22 (0 hand-out)
Time allowed:
UNIVERSITY OF SURREY©
Faculty of Arts & Social Sciences Surrey Business School Postgraduate Programmes in Management
MANM304: Operational Analytics
FHEQ Level 7 Examination
This is an online exam available over a period of 2 hours 2 hours
Answer all FOUR questions
Where appropriate the mark carried by an individual part of a question is indicated in square brackets [ ].
Calculators are permitted Additional materials: Open book
Semester 2 2021/2
©Please note that this exam paper is copyright of the University of Surrey and may not be reproduced, republished or redistributed without written permission
1
MANM304/7/SEMR2/21/22 (0 hand-out)
1 Cake shop – integer program [25/100].
A small local cake shop, Bob’s buns, produces a range of pastry products, including doughnuts and danishes. They make the two products in large pans. You have been asked to try and work out how many pans of each product to make each day to maximise profit given the amount of flour and sugar the shop can store for each day’s production.
You have the following information:
1. The shop has a maximum of 25kg flour and 16kg of sugar per day to make the doughnuts/danishes.
2. Each pan of danishes mixture requires 5kg flour and 2kg sugar.
3. Each pan of doughnut mixture requires 5kg flour and 4kg sugar.
4. Each pan of danishes mixture can produce enough danishes to make £3 profit per pan.
5. Each pan of doughnut mixture can produce enough danishes to make £4 profit per
pan.
6. From historical data, you can sell a maximum of four pans of danishes per day.
a) Make a table of the essential information.
b) Formulate a linear programming model, stating the objective function and constraints.
c) Use the graphical solution technique to find the optimal solution, that is the maximum profit that can be generated per day given the above constraints. Draw the graph and calculate the maximum profit.
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2
[5 marks] [10 marks]
[10 marks]
MANM304/7/SEMR2/21/22 (0 hand-out)
2 Data Visualisation [25/100]
a) What makes a good data visualisation?*
b) You are a data analyst in a big service management company. You have been asked to present data from a satisfaction survey of managers within various customers’ companies (see table below). Design a data visualisation that communicates the main message that, despite good performance for the other customers, “The satisfaction of managers within Customer B has markedly dropped in the past year.”
Your data visualisation should use a relevant graph type, be professionally presented, and include all relevant labels. You can submit your answer either as a hand drawing or a graph designed in the software of your choice.
Table 1: Customer satisfaction in
2020 and 2021 for four customers A-D.
[10 marks]
[15 marks]
Name
Customer A Customer A Customer B Customer B Customer C Customer C Customer D Customer D
Year
% satisfied
% not satisfied
2020
2021
2020
2021
2020
2021
2020
2021
48
67
74
52
67
85
39
57
52
33
26
48
33
15
61
43
*As a rough rule of thumb it should take you about 10 minutes to answer part (a), which should translate into a word count of between 150-300 words. You may also use diagrams to aid your answer.
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3
MANM304/7/SEMR2/21/22 (0 hand-out)
3 Walk In barbers queueing model – M/M/c [25/100].
A barbers in London does not book appointments for haircuts, but rather simply allows people to walk in and wait until a barber is free. On Saturdays it is staffed so that there are five barbers available to cut hair at any one time. The interarrival time of customers is 4 minutes (exponentially distributed). On average, each barber can cut the hair of 5 customers per hour (again exponentially distributed).
a. For the current five-barber service, state the arrival rate, service rate, interarrival time and service time. What is the current utilisation? Is the system stable?
[5 marks]
b. On average how many customers are in the barbers at any one time? How many customers are in the queue? How many are having their hair cut by a barber?
[10 marks]
c. On average how long is a customer in the queue waiting to see a barber? State your answer in minutes.
[3 marks]
d. In order to save money and resources, the manager of the barbers wants to see if it is feasible to have only 4 barbers at any one time, rather than five. If the manager reduces the number of barbers to 4, what will be the utilisation of the barbers, and what will be the average number of customers in the queue? What will be the average time a customer spends in the queue (state your answer in minutes)? Is the system stable?
[7 marks]
Note: Use the M/M/c queueing model: assume that P0 = 0.046647 for five barbers and 0.037736 for four barbers; Little’s law: ���=λ���, ��� =λ���, ��� =λ���, ���= λ, ��� =
λμ(λ/μ)��� .���,���=��� +λ,���=���+���. (���−1)!(���μ−λ)2 0 ��� μ ��� ���
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��� ��� ��� ��� ���μ ���
4
MANM304/7/SEMR2/21/22 (0 hand-out)
4 Estimating risk of losses – Risk Analysis [25/100].
You are a risk analyst in a large engineering company that wishes to bid for a large project to build a new submarine for the US Navy. As part of the bid process the company has asked you to conduct a risk assessment of potential financial losses.
Speaking with the bid leader, project managers and engineers, you have identified four main risks (A-D). Risk A-C will incur financial penalties due to delays in production. In contrast, Risk D encapsulates manufacturing faults that will require rebuilding substantial sections of the submarine. Quality controls minimise the likelihood of manufacturing faults, but if faults do occur they are very expensive to fix.
The engineers have given you the following estimates for each of the four risks:
1. Risk A has a 40% chance of losing between $4k-$6k (most likely $5k).
2. Risk B has a 72% chance of losing between $190k-$200k (most likely $195k).
3. Risk C has a 26% chance of losing $500k-$520k (most likely $510k).
4. Risk D has a 1% chance of losing $15M-$20M (most likely $17M).
As per company policy, you assess the risk of each project using the project risk matrix (see Figure 1 below).
Figure 1: The project risk matrix used by the company to estimate the frequency and severity of losses for individual risks. The scores given in the boxes are the risk scores calculated from the formula Risk Score = Likelihood Score x Consequence Score.
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5
MANM304/7/SEMR2/21/22 (0 hand-out)
a) What are the likelihood, consequence and risk scores for each project?
b) Calculate the expected value losses for each project (use the most likely values of loss in your calculation). What is the total expected loss if the company wins all four projects?
[5 marks]
c) Compare the rankings of risk from parts (a) and (b). Are there any inconsistencies? If so, explain how the inconsistency/inconsistencies arose.
[5 marks]
Given the potentially large losses associated with Risk D you decide to conduct a Monte Carlo simulation model of the risks to get a more accurate assessment.
d) Write out an appropriate formula that will derive the joint probability distribution for the losses to the project if one or more risks occur. (You do not need to calculate the answer, simply provide the formula).
[5 marks]
The company is naturally most concerned about Risk D, and wants to know the chances of incurring a loss greater than $18M. You plot the cumulative density function of the loss distribution (see Figure 2 below).
Figure 2: Cumulative distribution of estimated losses if Risk D occurs.
e) What is the probability of the project incurring a loss greater than or equal to $18M because of Risk D?
[5 marks]
[END OF EXAM]
6
[5 marks]
