1.     Briefly explain each of the following topics from the viewpoint of Operational Research/Management Science:

(a)  Using simulation to estimate the effect of segregating passengers arriving at a major international airport by COVID vaccination status before they            encounter passport/immigration control. (9 marks)

(b)  A specific and practical problem situation with which you are familiar where one of the inventory control techniques discussed in the subject guide might be used. (9 marks)

(c)  A specific and practical problem situation with which you are familiar (but     different from that considered in part (b) above) where the analytic hierarchy process might be used. (7 marks)

Note here that for this question no credit will be obtained for repeating material which is given in the subject guide. Your answer to this question should be limited to 2 pages for each of the three parts (so at most 6 pages in total).

2.       (a)     Apply Strategic Choice to one problem with which you are familiar. (12 marks)

(b)     Apply Soft Systems Methodology to one problem with which you are

familiar (where this problem must be distinctly different from the problem considered in part (a) of the question). (13 marks)

Note here that for this question no credit will be obtained for using the crime problem as given in the subject guide. Your answer to part (a) should be limited to 5 pages, your answer to part (b) limited to 5 pages.

3.        (a)

Solve the following linear program graphically using an iso-cost/iso-profit line. The vertices (corners) of the feasible region should be clearly          labelled A,B,C etc.

Minimise

Subject to

z = 4y - x

x + 2y ≥ 9

x + y ≤ 7

-x – 2y ≤ -5

x,y ≥ 0

Constraint 1

Constraint 2

Constraint 3

Copy the tables shown below into your answer and fill in the values required. (18 marks)

(b)   If constraint 3 now becomes -x – 2y ≤ - 10 then indicate the new feasible

region by labelling its corners using M,N,O etc.  Copy the table shown below into your answer and fill in the values required. (7 marks)

4.        Choose a single company with which you are familiar to discuss how four            different Management Science Methods approaches (as discussed in the subject guide) could realistically be used by the company to improve the effectiveness of their operations. You should clearly discuss in your answer the company chosen and its operations so that a person unfamiliar with it understands it before            discussing how your four chosen approaches could be applied in this company. (25 marks)

Note here that for this question no credit will be obtained for repeating material given in the subject guide. Your answer to this question should be limited to 5 pages.

5.     A company is trying to allocate its limited resources to a number of different          projects. It has three resources (labelled R1, R2 and R3 respectively) and three    projects to which they can be allocated (labelled P1, P2 and P3 respectively).  For each unit of each resource allocated to a project the project duration is reduced.   The table below shows the time reduced (in hours) per unit of resource allocated  to a project. For example allocating one unit of resource R2 to project P3 reduces the project duration for P3 by 1.4 hours.

It is believed that the company has available 1200 units of resource R1, 1500 units of resource R2 and 900 units of resource R3.

Technological restrictions mean that for every 3 units of resource R3 allocated to project P3 at most 2 units of resource R2 can be allocated to project P3.

The company would like to use goal programming to allocate resources to projects and ideally would allocate enough resource to each project so as to reduce the      duration of each individual project by 1200 minutes. However they accept it may    be necessary to deviate from this ideal, but are currently uncertain as to the           weights they would use for deviations in any goal program. However they are clear that project P1 is the most important project, followed by project P2, with project    P3 being the least important project.

An additional condition that needs to be considered is that a company goal is to reduce the total project duration time (over all three projects) by 3600 minutes.

(a)   Formulate this problem as a weighted goal program with linear constraints.

Note here that you should not attempt to solve this problem numerically or attempt to simplify any linear equations that you give. (18 marks)

(b)    How does your formulation change if instead of using goal programming you

formulate the problem as described above but using linear programming (so do not include goal deviation variables)? What might be the advantages and disadvantages of doing this? Note here that you should not attempt to solve this problem numerically or attempt to simplify any linear equations that you give. (7 marks)

6.     A retail organisation is reviewing the performance of its various branches using data envelopment analysis. These branches are stores that sell items to the     general public. The data that they have collected for these branches is shown  below.

For example branch C last year had 45,700 customers, made a profit of 20.1 million UK pounds and employed (on average) 20 employees.

(a)    Apply data envelopment analysis to compare the relative performance of

these branches using the data shown above. Copy the table shown below into your answer and fill in the efficiencies and reference sets (where         appropriate). (12 marks)

(b)    A colleague has raised two separate objections to your analysis. Firstly, that

profit (total revenue minus total cost) already includes employee cost, on      average £50,000 per employee after accounting for various direct employee costs including salary and pension/medical benefits. Other branch costs are usually estimated to be 300% of employee costs. So using the number of     employees in your analysis is incorrect. Rather your analysis should account for employee cost. How would you respond to this objection? Would it alter   your conclusions as in the table you gave in your answer to part (a) above. If so how?

Their second objection is that there is a statistically significant positive           correlation between the number of customers and the number of employees, both being related to the size of the retail branch. They argue that this            invalidates using both of these factors together; rather you should use one or the other. How would you respond to this objection? Would it alter your          conclusions as in the table you gave in your answer to part (a) above. If so    how? (13 marks)

7.       A company is considering using Markov theory to analyse consumers switching between the five different brands of washing aids which it markets. All of these washing aids are designed to make washed clothes clean and fresh, but use    different approaches. Two of these aids (A and B), are powder based. A further two (C and D), are based on liquid filled tablets. The final aid (E) is just liquid    based.

The current market shares for the five washing aids are 10%, 20%, 35%, 25% and 10% for aids A,B,C,D and E  respectively. Market research has produced the data shown below for the probability of customers switching between        washing aids every six months.

Here, for example, there is a probability of 0.07 that a customer switches from aid B to aid C.

(a)       Copy the following table into your answer and fill in the market shares for

these brands after six months . (3 marks)

(b)       Copy the following table into your answer and fill in the long-run market

shares for these brands . (22 marks)