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经济代写-ECO00030M
时间：2021-04-19
Page 1 of 7
Module Code
ECO00030M
MSc Degree Examinations 2020-1
Department:
Economics
Title of Exam:
Management Decision Analysis
Time Allowed: 24 Hours
PLEASE NOTE: Submissions up to 30 minutes late will receive a penalty
deduction of five marks. Submissions late by more than 30 minutes will not be
marked.
Time Recommended:
We would expect this to last two hours
Word limit:
There are no word limits.
Allocation of Marks:
The marks for each question are listed next to the question. Section A is weighted
at 85% and Section B is weighted 15%.
Instructions for Candidates:
Candidates should attempt to answer ALL questions of Section A.
ONE question from Section B should be answered.
If you attempt more than ONE question from Section B, only the first answer of
Section B the order in which it appears in the script, will be marked unless clearly
crossed out.
Any answers you do not wish to be included in the marking, must be clearly
crossed out
Page 2 of 7
A note on Academic Integrity
We are treating this online examination as a time-limited open assessment. You are
therefore permitted to refer to written, and online materials, to aid you in your answers.
However, you must ensure that the work you submit is entirely your own, and for the whole
time the assessment is live you must not:
● communicate with departmental staff on the topic of the assessment
● communicate with other students on the topic of this assessment
● seek assistance with the assignment from the academic and/or disability support
services, such as the Writing and Language Skills Centre, Maths Skills Centre and/or
Disability Services. (The only exception to this will be for those students who have
been recommended an exam support worker in a Student Support Plan. If this
applies to you, you are advised to contact Disability Services as soon as possible to
discuss the necessary arrangements)
● seek advice or contribution from any third party, including proofreaders, friends, or
family members.
We expect, and trust, that all our students will seek to maintain the integrity of the
assessment, and of their award, by ensuring that these instructions are strictly followed.
Failure to adhere to these requirements will be considered a breach of the Academic
Misconduct regulations, where the offences of plagiarism, breach/cheating, collusion and
commissioning are relevant - see AM.1.2.1” (Note this supersedes section 7.3 of the Guide
to Assessment).
Page 3 of 7
ECO00030M Management Decision Analysis
Section A (85 marks)
Candidates should attempt to answer ALL questions in this section.
1. [35 marks] Consider the following linear programming problem.
Minimise 81 + 62 + 3
Subject to 4 1x + 3 2x = 20
1x + 2x ≤ 8
1x + 53 ≥ 30
321 ,, xxx 0≥
(a) Use the simplex method to solve the minimisation problem. [20
marks]
(b) Determine the range of optimality for C1, i.e., the coefficient of x1 in
the objective function. How does the change in the value of the
coefficient C1 affect the value of the objective function? Which
constraints are binding? [10 marks]
(c) Can you solve the problem without using the simplex or the
graphical solution methods? Explain your method. [5 marks]
Turn Over
Page 4 of 7
2. [20 marks] VGKuality Furniture purchases a component used in the
manufacture of furniture directly from the supplier. VGKuality’s furniture
production operation, which is operated at a constant rate, will require
800 units of that component per year. Assume that the ordering costs
are £150 per order, and the annual holding cost is £3 per unit.
VGKuality has 250 working days per year. Answer the following
inventory policy questions.
(a) Firstly, consider the case that planned shortages are not
permitted. Then, what is the EOQ (economic order quantity) for
this component? What are the total annual holding and ordering
costs associated with your recommended EOQ? [5 marks]
(b) Next suppose that VGKuality decided to operate with a backorder
inventory policy. Backorder costs are estimated to be £20 per unit
per year. Identify in this case the following: the minimum cost
order quantity, the maximum number of backorders, and the total
annual cost. If the manager adds constraints that no more than 25
per cent of the units can be back ordered and that no customer
will have to wait more than 15 days for an order, should the
backorder inventory policy be adopted? [10 marks]
(c) Is the backorder inventory policy always better than the standard
EOQ policy without the planned shortages? And why? [5 marks]
Page 5 of 7
3. [30 marks] Describe a situation that involves multicriteria decisions such
that it can be analysed by the method of goal programming, and
construct a model to analyse the situation accordingly. Note that the
situation that you are going to describe should be different from the
examples that we have discussed in the lectures and exercises. You
should describe the situation clearly and in detail, but you are not
required to solve the model here.
Turn Over
Page 6 of 7
Section B (15 marks)
Candidates should attempt to answer only ONE question in this section.
4. [15 marks]
(a)
The matrix of transition probabilities below deals with consumers’
brand loyalty to supermarket Borrison and supermarket Vesco.
Current
Purchase
Next Purchase
Borrison Vesco
Borrison 0.90 0.10
Vesco 0.05 0.95
(i)
What are the projected market shares for the two
supermarkets? [5 marks]
(ii)
Suppose in the market there are 3,000 consumers. How
many customers will switch supermarkets on the next
purchase after a large number of periods? [2 marks]
(b) Suppose now a new supermarket, Osda, is founded such that the
transition probabilities become as follows.
Current
Purchase
Next Purchase
Borrison Vesco Osda
Borrison 0.80 0.10 0.10
Vesco 0.05 0.75 0.20
Osda 0.40 0.30 0.30
(i) What are the new long-run market shares? [5 marks]
(ii) Which supermarket will suffer more from the introduction of
the new supermarket? Explain. [3 marks]
Page 7 of 7
5. [15 marks] A company has five departments, 1, 2, 3, 4 and 5. The
management board is considering to appoint five of the following six
managers (Alice, Bob, Cathy, Damian, Edith and Felix) to these five
departments, respectively, such that one department will have one
manager, and one manager can lead at most one department. Their
expected performance, measured in the annual profit (in thousands of
pounds) of the departments are shown in the following table. Note that for
certain reasons, Bob can lead neither department 1 nor department 3. The
management board is considering the optimal assignment of allocating the
departments to the managers to maximise the expected total profit of the
company.
Department
Manager
1
2
3 4 5
Alice 65 90 51 55 16
Bob - 81 - 71 22
Cathy 67 85 66 77 20
Damian 77 91 61 85 12
Edith 66 57 81 77 10
Felix 70 80 72 63 18
(a) Formulate the above problem as a Linear Programming problem. [5
marks]
(b) Use the Hungarian method to find the optimal assignment. (Note
that you should carefully show the steps of the calculations.) Is it a
unique solution? If not, then please also specify any alternative
optimal assignment. [10 marks]
END OF EXAM
学霸联盟
Module Code
ECO00030M
MSc Degree Examinations 2020-1
Department:
Economics
Title of Exam:
Management Decision Analysis
Time Allowed: 24 Hours
PLEASE NOTE: Submissions up to 30 minutes late will receive a penalty
deduction of five marks. Submissions late by more than 30 minutes will not be
marked.
Time Recommended:
We would expect this to last two hours
Word limit:
There are no word limits.
Allocation of Marks:
The marks for each question are listed next to the question. Section A is weighted
at 85% and Section B is weighted 15%.
Instructions for Candidates:
Candidates should attempt to answer ALL questions of Section A.
ONE question from Section B should be answered.
If you attempt more than ONE question from Section B, only the first answer of
Section B the order in which it appears in the script, will be marked unless clearly
crossed out.
Any answers you do not wish to be included in the marking, must be clearly
crossed out
Page 2 of 7
A note on Academic Integrity
We are treating this online examination as a time-limited open assessment. You are
therefore permitted to refer to written, and online materials, to aid you in your answers.
However, you must ensure that the work you submit is entirely your own, and for the whole
time the assessment is live you must not:
● communicate with departmental staff on the topic of the assessment
● communicate with other students on the topic of this assessment
● seek assistance with the assignment from the academic and/or disability support
services, such as the Writing and Language Skills Centre, Maths Skills Centre and/or
Disability Services. (The only exception to this will be for those students who have
been recommended an exam support worker in a Student Support Plan. If this
applies to you, you are advised to contact Disability Services as soon as possible to
discuss the necessary arrangements)
● seek advice or contribution from any third party, including proofreaders, friends, or
family members.
We expect, and trust, that all our students will seek to maintain the integrity of the
assessment, and of their award, by ensuring that these instructions are strictly followed.
Failure to adhere to these requirements will be considered a breach of the Academic
Misconduct regulations, where the offences of plagiarism, breach/cheating, collusion and
commissioning are relevant - see AM.1.2.1” (Note this supersedes section 7.3 of the Guide
to Assessment).
Page 3 of 7
ECO00030M Management Decision Analysis
Section A (85 marks)
Candidates should attempt to answer ALL questions in this section.
1. [35 marks] Consider the following linear programming problem.
Minimise 81 + 62 + 3
Subject to 4 1x + 3 2x = 20
1x + 2x ≤ 8
1x + 53 ≥ 30
321 ,, xxx 0≥
(a) Use the simplex method to solve the minimisation problem. [20
marks]
(b) Determine the range of optimality for C1, i.e., the coefficient of x1 in
the objective function. How does the change in the value of the
coefficient C1 affect the value of the objective function? Which
constraints are binding? [10 marks]
(c) Can you solve the problem without using the simplex or the
graphical solution methods? Explain your method. [5 marks]
Turn Over
Page 4 of 7
2. [20 marks] VGKuality Furniture purchases a component used in the
manufacture of furniture directly from the supplier. VGKuality’s furniture
production operation, which is operated at a constant rate, will require
800 units of that component per year. Assume that the ordering costs
are £150 per order, and the annual holding cost is £3 per unit.
VGKuality has 250 working days per year. Answer the following
inventory policy questions.
(a) Firstly, consider the case that planned shortages are not
permitted. Then, what is the EOQ (economic order quantity) for
this component? What are the total annual holding and ordering
costs associated with your recommended EOQ? [5 marks]
(b) Next suppose that VGKuality decided to operate with a backorder
inventory policy. Backorder costs are estimated to be £20 per unit
per year. Identify in this case the following: the minimum cost
order quantity, the maximum number of backorders, and the total
annual cost. If the manager adds constraints that no more than 25
per cent of the units can be back ordered and that no customer
will have to wait more than 15 days for an order, should the
backorder inventory policy be adopted? [10 marks]
(c) Is the backorder inventory policy always better than the standard
EOQ policy without the planned shortages? And why? [5 marks]
Page 5 of 7
3. [30 marks] Describe a situation that involves multicriteria decisions such
that it can be analysed by the method of goal programming, and
construct a model to analyse the situation accordingly. Note that the
situation that you are going to describe should be different from the
examples that we have discussed in the lectures and exercises. You
should describe the situation clearly and in detail, but you are not
required to solve the model here.
Turn Over
Page 6 of 7
Section B (15 marks)
Candidates should attempt to answer only ONE question in this section.
4. [15 marks]
(a)
The matrix of transition probabilities below deals with consumers’
brand loyalty to supermarket Borrison and supermarket Vesco.
Current
Purchase
Next Purchase
Borrison Vesco
Borrison 0.90 0.10
Vesco 0.05 0.95
(i)
What are the projected market shares for the two
supermarkets? [5 marks]
(ii)
Suppose in the market there are 3,000 consumers. How
many customers will switch supermarkets on the next
purchase after a large number of periods? [2 marks]
(b) Suppose now a new supermarket, Osda, is founded such that the
transition probabilities become as follows.
Current
Purchase
Next Purchase
Borrison Vesco Osda
Borrison 0.80 0.10 0.10
Vesco 0.05 0.75 0.20
Osda 0.40 0.30 0.30
(i) What are the new long-run market shares? [5 marks]
(ii) Which supermarket will suffer more from the introduction of
the new supermarket? Explain. [3 marks]
Page 7 of 7
5. [15 marks] A company has five departments, 1, 2, 3, 4 and 5. The
management board is considering to appoint five of the following six
managers (Alice, Bob, Cathy, Damian, Edith and Felix) to these five
departments, respectively, such that one department will have one
manager, and one manager can lead at most one department. Their
expected performance, measured in the annual profit (in thousands of
pounds) of the departments are shown in the following table. Note that for
certain reasons, Bob can lead neither department 1 nor department 3. The
management board is considering the optimal assignment of allocating the
departments to the managers to maximise the expected total profit of the
company.
Department
Manager
1
2
3 4 5
Alice 65 90 51 55 16
Bob - 81 - 71 22
Cathy 67 85 66 77 20
Damian 77 91 61 85 12
Edith 66 57 81 77 10
Felix 70 80 72 63 18
(a) Formulate the above problem as a Linear Programming problem. [5
marks]
(b) Use the Hungarian method to find the optimal assignment. (Note
that you should carefully show the steps of the calculations.) Is it a
unique solution? If not, then please also specify any alternative
optimal assignment. [10 marks]
END OF EXAM
学霸联盟
