1. A motorist is using the AHP to choose a new car from three possible models: an Arrow, a Bestmobile and a Commuter. The choice will be based on just two attributes, Cost and Style.

When asked to compare the cost of the cars, the motorist makes the following statement: On cost, the Bestmobile is "weakly preferred" to the Arrow, but the Arrow is "weakly preferred" to the Commuter. Also the Bestmobile is "extremely preferred" to the Commuter.
On style, the Arrow is "very strongly preferred" to the Bestmobile, but the Commuter is "weakly preferred" to the Arrow. Also the Commuter is "extremely preferred" to the Bestmobile.

a) Construct a hierarchy to present the decision problem (using a computer or by hands and then scanning the page)

2. Imagine you have won a holiday for two people in a magazine competition and you have been given the choice of five holiday's destinations. The names and details of these destinations are shown below. Use the method of Even Swaps to determine which destination you would choose on the basis of the information that has been supplied.

3. A chemical company is expanding its operations and disused woolen mill is to be converted into a processing plant. Four companies have submitted designs for the equipment which will be installed in the mill and a choice has to be made between them. The manager of the chemical company has identified three attributes which he considers to be important in the decision: cost, environmental impact, and reliability. He has assessed how well each design performs on each attribute by allocating values on a scale from 0 (the worst design) to 100 (the best). These values are shown below, together with the costs which will be incurred if a design is chosen.

The manager is having difficulty in allocating weights to the two benefit attributes. Assuming that the two weights sum to 100 and that mutual preference independence exists between the attributes, perform a high level sensitivity analysis to show how the design offering the highest value for aggregate benefit will vary depending upon the weight which has been allocated to environment impact. (10% of the grade)

b. Eventually, the manager decides to allocate environment impact a weight of 30 and reliability a weight of 70. By plotting the benefits and costs of the design on a graph, identify the design which lies on the efficient frontier.

4. One of the criticisms of the AHP is that the introduction of new alternatives can change the ranking of existing alternatives. Under what circumstances, if any, is this likely to be reasonable?

5. A manager is hoping to appoint a new assistant and decides to use AHP to rank the applicants for the job. Then, as a check, she decides to repeat the process using SMART. She is surprised to find that the ranking of the applicants derived from the AHP differs significantly from the ranking suggested by the SMART analysis. Discuss why the differences.