### Clearly describe Soft Systems Methodology (SSM) with particular emphasis on the underlying assumptions.

Illustrate SSM by applying it to any two examples with which you are familiar.

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

(a) SCM

(b) Benefits of simulating customer checkout operations at a supermarket.

(c) Utilities, with reference to a risk-seeking decision-maker.

- Describe what you understand by the following in relation to methodological issues that arise in Operational Research/Management Science:

(a) The benefits of an OR approach to decision problems.

(b) Cost versus decision quality.

- (a) The payoff table below shows for a company the final year end profits expected (£m) from four possible choices (A, B, C and D) with respect to three possible scenarios (S1 to S3 respectively) for the forthcoming year.

Here, for example, if the company makes choice B (and it can only choose one of A, B, C or D) and the scenario for the forthcoming year turns out to be S2 then it makes a profit of £18m. Scenario S1 is believed to have probability

0.3 and scenario S3 is believed to have a probability 0.2.

Copy the table shown below into your answer book and fill in the choice that should be made under each criterion and the associated value.

Based on your analysis which choice would you recommend the company makes?

(b) In a single-server queueing system with an exponential service time distribution and a Poisson arrival distribution customers arrive at an (average) rate of 100 per hour. The server takes (on average) 25 seconds to serve a customer.

- Assuming that the system is in a steady state copy the table shown below into your answer book and fill in the corresponding numeric values.
- Explain how knowing the average number of customers in the queue could help you manage the system.
- A company X streaming films over the Internet uses Markov’s theory to try and understand how its market share changes over time. The company has two main competitors (Y and Z) and past estimates of the probability of a

customer making a transition between companies when they come to stream a film are:

Here, for example, the probability that a customer switches from company Y to company Z is 0.29. On average a customer streams a film once a week.

(a) Copy the table shown below into your answer book and fill in the market share for company X after two weeks if the current market shares are 40%, 40% and 20% for companies X, Y and Z respectively.

(b) Copy the table shown below into your answer book and fill in the long-run prediction for the market shares for each of the three companies.

(c) Company X is considering merging with company Y to create a new company (XY). In this case they estimate that the matrix for the probability of a customer making a transition between companies when they come to stream

a film will be:

Here, for example, the probability that a customer switches to company Z from the company, XY is 0.60.

Copy the table shown below into your answer book and fill in the long run prediction for the market shares for each of the two companies.

(d) Considering the transition matrices given above do you think it is plausible that the proposed merged company XY only retains 40% of its customers at each switch?

- A company requires a component Z at the rate of 1950 units per week. Each unit costs £8 when purchased from the current supplier. The ordering cost associated with placing an order with the current supplier is believed to be approximately £13. The interest rate is assumed to be 5% per year and the warehousing costs associated with storage and maintenance are 12% of the cost of a unit a year. Assume the company works 52 weeks a year.

What order quantity in terms of ordering Z from your supplier would you recommend and what would be the cost (per year) of your recommendation?

The company believes that it is possible that the ordering cost associated with placing an order with the current supplier is actually £14. They are unsure as to the precise value for ordering cost. Would this alter your recommendation? Give your reasons.

For the remaining parts of this question assume the ordering cost is £13.

A new directive has been issued by the managing director of the company which states that, in order to save on overhead costs, the company will place orders either once a week, or once every two weeks. You know that if you order once every two weeks your supplier will give you a 3% discount on the cost of a

component. What order quantity in terms of ordering Z from your supplier would you recommend and what would be the cost (per year) of your recommendation?

What would the discount from the supplier have to be before you were indifferent between ordering weekly and ordering once every two weeks?

- A central authority that oversees seven branches (A to G) is reviewing their performance. The data they have collected for these branches is shown below.

For example branch F last year had a total cost of £10 million, employed 230 people and had 890 customers.

Copy the table shown below into your answer book and fill in the efficiencies and reference sets (where appropriate).

If you had overall managerial responsibility for these branches what questions might be raised in your mind as a result of your analysis?

Briefly discuss how you might go about starting a DEA study for an organization with a number of branches.

- Solve the following linear program graphically using an iso-cost/iso-profit line, clearly indicating the feasible region.

Minimise z = 3x + 7y

Subject to 2x + y ≥ 13 Constraint 1

2x – 5y ≤ 7 Constraint 2

x,y > 0

Discuss three areas where large linear programs arise.