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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