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 weight, though, can reveal whether a decision maker must make a more precise judgment. Reconsider the summer-job example described and analyzed in Chapter 4 (pages 129-136). In the analysis, we used trade-off weights of ks = 0.60 for salary and kf = 0.40 for fun (see Figure 4.36).
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 to 0.25, depending on the value of ks.) Perform a sensitivity analysis on the expected overall score for the two jobs by varying ks over this range. Is the forest job preferred for all values of ks between 0.50 and 0.75?