Question One A group of medical professionals (doctors) is considering the construction of a small private hospital. If medical demand is high (i.e. if there is a favourable market for the hospital),...

Question One

A group of medical professionals (doctors) is considering the construction of a small private hospital. If medical demand is high (i.e. if there is a favourable market for the hospital), the doctors could realise a net profit of £10m.



If the market is not favourable, they could lose £4m.



Of course, they do not have to proceed at all in which case there is no cost.



In the absence of any market data, the best the doctors and their advisers can estimate is that there is a 50:50 chance that the hospital will be successful.



(a)    Draw a decision tree that describes the above decision problem and advise the doctors on the optimal decision.

                                        (10 marks)


The same group of medical professionals (doctors) as above, have been approached by a market research firm that offers to perform a study of the market (at a fee of £50,000). The market researchers claim their experience has enabled them to use Bayes’ theorem to make the following six statements of probability:

1.    Probability of a favourable market given a favourable study = 0.82
2.    Probability of an unfavourable market given a favourable study = 0.18
3.    Probability of a favourable market given an unfavourable study = 0.11
4.    Probability of an unfavourable market given an unfavourable study = 0.89
5.    Probability of a favourable research study = 0.55
6.    Probability of an unfavourable research study = 0.45


(b)    Develop a new decision tree for the medical professionals to reflect the options now open with the market study.

(10 marks)


(c) Use the Expected Monetary Value (EMV) approach and recommend an optimal strategy.

(10    marks)
(d)Determine the expected value of sample information.

(5    marks)


(e)    Advise the medical professionals on the maximum amount that they should be willing to pay for the market study.

(5 marks)


(e) Compare and contrast decision tree analysis and use of influence diagrams in managerial decision making involving risk and uncertainty.   (10 marks)




Question Two


A London based local authority owns a tramway system and the tram operators are under pressure to increase passenger numbers. They have to make a decision on whether to lower fares in an attempt to increase passenger numbers.



If they decide to reduce fares they will then have to decide whether to launch an advertising campaign on local television to increase awareness of the fare reduction.



If fares remain the same then it is estimated that there is a 0.7 probability that the mean number of passengers carried per day over the next year will equal to 20 000 and a 0.3 probability that it will decline to 15 000.



The annual profits associated with these passenger numbers are estimated to be £3million and £1million, respectively.


If the fares are reduced, but television advertising is not used, then it is thought that there is a 0.6 probability that the mean number of passengers carried will increase to 25 000 and a 0.4 probability that it will increase 22 000. The resulting profits generated by these passenger numbers are estimated to be £2million and £1.7 million, respectively.



Advertising the fare reduction on television would increase the probability of an increase to a mean of 25 000 passengers to 0.8 and reduce the probability that the mean will be 22 000 to 0.2. However, it would reduce the profits associated with these mean passenger numbers by £0.6 million. The tram operating company’s objectives are to maximise profit and to maximise passenger numbers.  (This second objective is in place as local authority wish to bring forward  environmental benefits such as increased air quality and reduced traffic congestion).



(a)    Utility functions for the mean numbers of passengers carried and the profit have been obtained from the trams operator’s Chief Executive. and these are given below: