An important application of sensitivity analysis occurs in problems involving multiple attributes. Many decision makers experience difficulty in assessing trade-off weights. A sensitivity analysis of the trade-off weights, though, can reveal whether a decision maker must make a more precise judgment. Reconsider the summer-job example described and analyzed in Chapter 4 of the book. In the analysis, we used trade-off weights of ks = 0.60 for salary and kf = 0.40 for fun (see Figure 4.28).

Suppose Sam Chu is uncomfortable with the precise assessment that ks = 0.60. Sam does believe, though, that ks could range from 0.50 up to 0.75. (Recall that ks and kf add up to 1, so by implication, kf can range from 0.50 t0 0.25, depending on the value of ks). Perform a sensitivity analysis on the expected overall score for the value of ks over this range. Is the forest job preferred for all values of ks between 0.50 and 0.75?

Summer Fun Level 5 (0.10) Overall Score 88.6 4 (0.25) 84.6 Forest Job 3 (0.40) 72.6 2 (0.20) 58.6 1 (0.05) 486 Average Amount of Work per Week 40 hours (0.35) 84.0 In-Town Job 34 hours (0.50) 30 hours (0.15) 48.0 24.0