JOB OFFERS Robin Pinelli is considering three job offers. In magazine survey of large cities that scores those cities trying to decide which to accept, Robin has as places for single professionals to live. Although the concluded that three objectives are important in this survey is not perfect from Robin's point of view, it does decision. First, of course, is to maximize disposable capture the main elements of her concern about the income-the amount left after paying for housing, quality of the singles community and available utilities, taxes, and other necessities. Second, Robin activities. Also, all three of the cities under wants to spend more time in cold weather climates consideration are included in the survey. enjoying winter sports. The third objective relates to Here are descriptions of the three job offers: the quality of the community. Being single, Robin would like to live in a city with a lot of activities 1. MPR Manufacturing in Flagstaff, Arizona. Dis- and a large population of single professionals. posable income estimate: $1,600 per month. Developing attributes for these three objectives Snowfall range: 150 to 320 cm per year. Magazine turns out to be relatively straightforward. score: 50 (out of 100). Disposable income can be measured directly by 2. Madison Publishing in St. Paul, Minnesota. Dis- calculating monthly takehome pay minus average posable income estimate: $1,300 to $1,500 per monthly rent (being careful to include utilities) for an month. (The uncertainty here is because Robin appropriate apartment. The second attribute is annual knows there is a wide variety in apartment rental snowfall. For the third attribute, Robin has located a prices and will not know what is appropriate and available until spending some time in the city.) FIGURE 4.47 Robin Pinelli's Disposable Income Snowfall Magazine decision tree. Income Snowfall (cm) Rating Rating Rating 100 (0.15) $1500 (0.60) 400 (0.15) Madison Publishing 75 100 (0.15) $1300 200 (0.70) (0.40) 400 (0.15 75 25 56 200 (0.70) 75 50 56 100 56 25 25 56 25 50 56 25 100 56 150 (0.15) 100 37.5 0 MPR Manufacturing 230 (0.70 100 57.5 0 320 (0.15) 100 80 0 Pandemonium Pizza 0 0 100 weight for the Snowfall range: 100 to 400 cm per year. Magazine score: 75. 3. Pandemonium Pizza in San Francisco, California. Disposable income estimate: $1,200 per month. Snowfall range: negligible. Magazine score: 95. Robin has created the decision tree in Figure 4.47 to represent the situation. The uncertainty about snowfall and disposable income are represented by the chance nodes as Robin has included them in the tree. The ratings in the consequence matrix are such that the worst consequence has a rating of zero points and the best has 100. Questions 1. Verify that the ratings in the e consequence matrix are proportional scores (i.e., that they were calcu- lated the same way we calculated the ratings for salary in the summer-fun example in the chapter). 2. Comment on Robin's choice of annual snow- fall as a measure for the cold- weather-winter-sports attribute. Is this a good measure? Why or why not? 3. After considering the situation, Robin concludes that the quality of the city is most important, the amount of snowfall is next, and the third is income. (Income is important, but the difference between $1,200 and $1,600 is not enough for income to be more important in this context.) Furthermore, Robin concludes that the weight for the magazine rating in in the consequence matrix should be 1.5 times the weight for the snow- fall rating and three times as much as the income rating. Use this information to calculate the weights for the three attributes and to calculate overall scores for all of the end branches in the decision 4. Analyze the decision tree using expected values. Calculate expected values for the three measures as well as for the overall score. 5. Do a risk-profile analysis of the three cities. Create risk profiles for each of the three attributes as well as for the overall score. Does any additional insight arise from this analysis? 6. What do you think Robin should do? Why? tree