Question 1. Decisions under Uncertainty

A company specializes in establishing local, privately run leisure centers throughout the country. Typically, the company will undertake considerable demographic analysis

and assess the potential for establishing such a center in a particular area. Areas targeted

generally, are those with a high proportion of middle-income families (young age profiles,

parents with professional occupations, car owners) and with poor or non-existent

public leisure facilities. The centers offer a range of sporting and related leisure facilities:

squash, badminton, swimming, gym, sauna together with a cafe and bar. The center facilities are offered on an annual membership basis. After some initial analysis, the company is considering building one such center in a particular area. Detailed planning permission has already been obtained, and financial support from the companys bank has been approved. On this specific site, the company is considering a range of options:

Option A: Build a large center offering a full range of facilities.

Option B: Build a medium-sized center now with a selected range of facilities. Over the

next two to three years, assess whether the center should be further expanded to the

full range of facilities.

Option C: Delay a decision about the size of the center until a more detailed market analysis has been completed (expected to take a further 12 months). At that time, a decision would be taken to build either a large center or a medium-sized center. This extra

market analysis would cost an additional 150 000.

To help in its analysis, the company has commissioned forecasts of the likely levels of use of the center and undertaken a financial assessment of the various options/outcomes.

Preliminary market research indicates that for Option A the chance of demand for the

centers facilities being high is 0.7, and of demand being low is 0.3. With high demand,

the company stands to make an estimated 950 000 profit. With low demand, it would

generate a loss of 700 000.

For Option B the probabilities of high and low demand remain the same. If demand does turn out to be low then the company has already decided it would not expand the center any further. The projected profit is 100 000. However, if demand turns out to be high, the company has a further option of expanding the center, although it has not yet decided if it should do this. If the company decided against expanding the center, the profit will remain 500 000. If the company decide to expand, it might be successful and generate an estimated profit of 650 000 but if it is not successful the company will lose 100 000. The chance of a further expansion being successful has been put at 0.9.

If more detailed market analysis is undertaken in Option C the probabilities of high and low demand change to 0.8 and 0.2 respectively, since the company will be able to target its marketing and advertising more precisely. However, after such analysis has been completed the company will still have to decide whether to build a large center (as in

Option A) or a medium-sized center (as in Option B), although in this latter case it would

not subsequently be worthwhile expanding the medium-sized center any further. For a

large center the financial outcomes are a profit of 950 000 if demand is high and a loss

of 700 000 if demand is low. If a medium-sized center is built the company estimates a

profit of 700 000 if demand is high but a profit of only 100 000 if demand is low.

1. Present the decision tree.
2. What is the best decision that will generate the maximum profit?