Assignment Ch2

Chap 2 Decision Analysis (Due Sept 22) 22 ) 1. Even though independent gasoline stations have been having a difficult time, Susan Solomon has  been thinking thinking about starting starting her own independent independent gasoline gasoline station. station. Susan’s Susan’s problem problem is to decide decide how large her station should be. The annual a nnual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following f ollowing table: SIZE OF FIRST GOOD MARKET($) FAIR MARKET($) POOR MARKET($) STATION  – 8,000 Small 40,000 15,000 8,000 Medium 75,000 28,000 18,000  – 18,000 Large 96,000 28,000 37,000  – 37,000 Very large 290,000 24,000 150,000  – 150,000 For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000. (a) Develop a decision table for this decision. (b) What is the maximax decision? (c) What is the maximin decision? (d) What is the equally likely decision? (e) What is the criterion of realism decision? Use an α value of 0.8.

(f) Develop an opportunity loss table. (g) What is the minimax regret decision?

2. Peter Martin is going to help his brother who wants to open a food store. Peter initially believes that there is a 50 –50 chance chance that his brother’s food food store would would be a success. success. Peter is considering doing a market research study. Based on historical data, there is a 0.82 0. 82 probability that the marketing research will be favorable given a successful food store. Moreover, there is a 0.71 probability that the marketing research will be unfavorable given an unsuccessful food store. (a) If the marketing research is favorable, what is Peter’s revised probability of a successful food store for his brother?

(b) If the marketing research is unfa vorable, what is Peter’s revised probability of a successful food store for his brother? (c) If the initial probability of a successful food store is 0.60 (instead of 0.50), find the  probabilities in parts parts a and b. 3. A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each e ach of these depends on whether the economy is good, fair, or  poor. A payoff table has been constructed constructed to illustrate illustrate this situation: situation:

INVESTMENT Fund A Fund B Probability

GOOD ECONOMY $5,000 $3,000 0.2

FAIR ECONOMY $1,000 $2,000 0.3

POOR ECONOMY -$2,500 0 0.5

(a) Draw the decision tree to represent this situation. (b) Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value? (c) Suppose there is question about the return of Fund A in a good economy. It could be higher or lower than $5,000. What value for this would cause a person to be indifferent between Fund A and Fund B (i.e., the EMVs would be the same)?

4. Mary is considering opening a new grocery store in town. She is evaluating three sites: downtown, the mall, and out at the busy traffic circle. Mary calculated the value of successful stores at these locations as follows: downtown, $250,000; the mall, $300,000; the circle, $400,000. Mary calculated the losses if unsuccessful to be $100,000 at either downtown or the mall, and $200,000 at the circle. Mary figures her chance of success to be 50% downtown, 60% at the mall and 75% at the circle. a.

Draw a decision tree for Mary and select her best alternative.

 b. Mary has been approached by a marketing research firm that offers to study the area to determine if another grocery store is needed. The cost of this study is $30,000. Mary believes there is a 60% chance that the survey result will be positive (show a need for another grocery store). Define SRP = survey results positive, SRN = survey results negative, SD = success downtown, SM = success at mall, SC = success at circle, SD’ = don’t succeed downtown, and so on. For studies of this

nature: P(SRP| success)=0.7; P(SRP| not success)=0.2. Calculate the revised probability for success and not success for each location, depending on survey results. c.

How much is the marketing research worth to Mary? Calculate the EVSI.

5. Explain the following two statements. Show both of the statements hold through the Thomson Lumber Company example on page 3 of the lecture note. a.

Minimum EOL will always result in the same decision as maximum EMV

 b. Minimum EOL = EVPI