1.       (a)     Apply both Journey Making and Strategic Choice to one problem with which you are familiar

(16 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).

(9 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 6 pages, your answer to part (b) limited to 3 pages.

2.       Briefly discuss each of the following topics from the viewpoint of Operational Research/Management Science:

(a) Using simulation to estimate the effect on public bus transport of enforcing a one metre separation between individuals

(9 marks)

(b) Two specific and practical problem situations with which you are familiar where the assumptions underlying optimisation are false

(7 marks)

(c) Using Markov processes to model the progress of a new, and previously unknown, disease in a population

(9 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).

3.     An  organisation  is  reviewing  the  performance  of  its  branches  using  data envelopment analysis. The data they have collected for these branches is shown below.

For example branch E last year employed 17 people and had 26,300          customers. The customer satisfaction score is a measure of how satisfied a

customer is with the branch (arrived at by surveying a random sample of        customers, approximately 1% of the number of customers a branch has). The higher the satisfaction score, the more satisfied customers are. Branch E, for example, had a satisfaction score of 18.6.

(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)    In a discussion with a colleague as to your analysis they have noted that

you have not included the fact that customer satisfaction is scored out of 25. They feel that this information should have been included in your       analysis, and would have altered the results. What would you say to        them?

(2 marks)

(c)    Another colleague has argued that customer satisfaction score is a wrong measure to use and you should use total satisfaction, defined as the         current customer satisfaction score multiplied by the number of                 customers. What would you say to them?

(5 marks)

(d)    The company CEO feels that only sampling approximately 1% of the       customers in a branch to get a customer satisfaction score is insufficient and could result in some branches being shown to be efficient when in    fact they are inefficient; or branches being classified as inefficient when  they are actually efficient. In support of their argument they have             produced the new customer satisfaction scores shown below based on a larger sample. What would you say to them?

4.  (a)       A company faces a decision as to whether to continue or not, with a

particular product it has developed. It can cease development of the       product, in which case all expenditure to date will be written off in the      company accounts. Alternatively it can decide to test market the product in a small geographic area. Over the next financial year test marketing is estimated to cost 5 (£’million). If the market for the product when test      marketed is favourable then the company will receive 7 (£’million) in        revenue. However if the market is unfavourable it will only receive 2.5     (£’million).

Alternatively the company could introduce the product to a wider market. Over the next financial year this is estimated to cost 15 (£’million). If the market for the product is favourable then the company will receive 23     (£’million) in revenue. However if the market is unfavourable it will only   receive 11 (£’million).

Assuming that the probability of the market being favourable is 0.40    represent this problem using a decision tree. What course of action for the company would you recommend based upon this decision tree?

(12 marks)

(b)       Copy the table shown below into your answer and fill it in with respect to

perfect information for the probability of the market being favourable.

(7 marks)

(c)       What would the probability of the market being favourable have to be if the expected value of perfect information was one half of the expected value with perfect information? Note that if no probability exists which   can achieve this you should clearly indicate why no such probability     exists.

(6 marks)

5.  (a)        Solve the following linear program graphically using an iso-cost/iso-profit

line, clearly indicating the feasible region.

Maximise

Subject to

z = 8x + 6y

2x + 5y ≤ 27

3x – 28y ≤ 19

x,y ≥ 0

Constraint 1

Constraint 2

Copy the tables shown below into your answer and fill in the values required.

(19 marks)

(b) In this linear program the objective, z = 8x + 6y, represents the total profit made by a company from producing two liquid chemical products             (chemical product X with a profit per litre of £8, chemical product Y with a profit per litre of £6). The company can either:

•    Increase the profit per litre on product X to £9; or

•    Increase the amount of resource available associated with the       right-hand side of constraint 1 from its current value of 27 to a new value of 29.

Based on the linear program given above which course of action would you recommend and why? Clearly explain the reasons for your              recommendation.

(6 marks)

6.     A company is using Markov theory to analyse switching between four different foods marketed as slimming aids. These slimming aids claim that with regular use they result in significant weight loss.

Individual customers who buy these sliming aids only switch (on average) once every four months. Market research has produced the data shown below for the probability of customers switching between slimming aids.