decision analysis

Questions on Decision Analysis

-------------------------------------------------

Problem 1

Morley Properties is planning to build a condominium development on St Simons Island, Georgia. The company is trying to decide between building a small, medium, or large development. The payoffs received for each size of development will depend on the market demad for condominiums in the area, which could be low, medium, or high. The payoff matrix for this decision problem is: Market Demand Size of Development Low Med High Small 400 400 400 Medium 200 500 500 Large -400 300 800 (Payoffs in 1,000s) The owner of the company estimates a 21.75% chance that market demand will be low, a 35.5% chance that it will be medium, and a 42.75% chance that it will be high. 1.) What decision should be made according to the EMV decision rule? Solve using a decision tree.

2.) Suppose that the utility function for the owner of Morely Properties can be approximated by the exponential utility function U(X) = 1 - e^(-x/R) where the risk tolerance value R=100 (in $1,000s) A. Convert the payoff matrix to utility values. B. What decision provides the owner of the company with the largest expected utility?

1) Solve calculating expected utilities (in a table)

2) Copy the worksheet from last week with the decision tree that uses EMVs into a separate worksheet of the same file.

3) Copy the tree in yet another worksheet and convert to expected utilities

4) Discuss/compare the three results and provide an explanation for possible differences.

Explanations: To convert the payoffs to utilities, plug in each payoff as x into the exponential utility function, using R=100 as given in the problem. 

Problem 2.

See the attached pdf file. Solve both part a) and b) using a decision tree in Solver. This decision scenario needs to include the "do nothing" option.

Problem 3.

The president of Pegasus Corporation is trying to decide which of three candidates (denoted as candidates A, B, and C) to hire as the firm’s new vice president of Marketing. The primary criteria the president is considering are each candidate’s leadership ability, interpersonal skills, and administrative ability. After carefully considering their qualifications, the president used AHP to create the following pairwise comparison matrices for the three candidates on the various criteria:

Next, the president of Pegasus considered the relative importance of the three criteria. This resulted in the following pairwise comparison matrix:

a. Use AHP to compute scores for each candidate on each of the three criteria, and to compute weights for each of the criteria.

b. Was the president consistent in making pairwise comparisons?

c. Compute the weighted average score for each candidate. Which candidate should be selected according to your results?