(7)

(a) Use an influence diagram to represent the following decision problem, stating any assumptions you have made.

ABC Chemicals are planning to start manufacturing a new pharmaceutical product. Initially, they must decide whether to go for large-scale or small-scale production. Having made this decision, the profits that they make will also depend on (i) the state of the economy over the next 2 years; (ii) whether or not a rival manufacturer launches a similar product; and (iii) the amount which ABC decides to spend on advertising the product (this decision will itself be influenced by the scale of production which ABC opt for, whether a rival product is launched and the state of the economy).

(b) Use your influence diagram to derive the outline of a decision tree which could be used to represent ABC’s problem.

(8) Draw an influence diagram for the following problem.

Hatton’s mail order company is planning to install a new computer system next year. Two possible systems are being considered: the Gamma II and the Elite. The Gamma II will mean that the company incurs higher initial costs than the Elite, but the total costs associated with the chosen system over its lifetime will also depend on whether the company decides to expand the computer system at some future date (the Gamma II system would cost less to expand). The expansion decision will be influenced by the level of sales achieved by the company over the next 3 years, while the level of sales will, in turn, be influenced by the size of the market and the amount of competition which Hatton’s has to face. It is thought that the size of the market will itself be influenced by the performance of the economy (e.g., a continued recession would depress the market). It is also thought that if the recession continues then a number of rivals will go out of business so the severity of competition will be less.