Question

John Smith has been thinking of starting a gasoline station business. Smith owns a piece of land near the intersection of two highways. But there are already a few gasoline stations nearby. He thinks that the annual returns will depend on two variables, the size of the station and a demand factor applicable to the area. After careful analysis, Smith develop the following payoff table: in thousands (K) SIZE DEMAND Goed $50 S80 S 100 $ 300 Small 2 Medium og Large a Fry Large GASOLINE STATION $20 S 30 $ 30 ez: Poor S-10 S-20 S-40 S-160 $ 25 For example, if Smith constructs a small station and the demand is fair, he will realize a net return of $20,000. Answer the following questions. Show work. 1. What is the solution from the point of view of: a. Perfect optimism (maximax)? b. Perfect pessimism (maximin)? c. Realism with a = .8? d. The criterion of conservatism (equal likelihood)? e. What is the minimax decision (criterion of regret)? f. On the basis of your calculations what would your decision be? Why? Explain. 2. John Smith constructed a market analysis that showed that the probability that the demand will be "good" is 50%, the probability that it will be "fair" is 30% and the probability that it will be "poor" is 20%. On that basis of this new information, by using a decision tree, answer the following questions: a. What is the expected value of each alternative? Which alternative should Smith choose from this point of view? b. What is the risk factor (o) of each alternative? Which alternative has minimum risk? c. Smith needs to make at least $20K to make a living. What is the probability of this event occurring for each alternative? (Use the Z-table) d. How about making at least $40K? (Use the Z-Table) e. Which alternative is the optimal one from the point of view of the coefficient of variation (cov)?

Answer 1

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Maximax Max. payoff $50 Alternative Demand Small Medium Large Very large Good $50 $80 $100 $300 Fair $20 $30 $30 $25 Poor ($10) ($20) ($40) ($160) $100 $300 The best alternative is very large Station. (6) Maximin Alternative Demand Small Medium Large Very large Good $50 $80 $100 $300 Fair $20 $30 $30 $25 P oor ($10) ($20) ($40) ($160) Min. payoff ($10) ($20) ($40) ($160) The best alternative is SmallStation. Realism (Hurwicz) Decision Rule Alternative Demand Small Medium Large Very large Good $50 $80 $100 $300 Fair $20 $30 $30 $25 Poor ($10) ($20) ($40) ($160) Min ($10) ($20) ($40) ($160) Max $50 $80 $100 $300 a*Max + (1 - a)*Min $38.0 $60.0 $72.0 $208.0 The best alternative is very large Station. (d) Equal likelihood Alternative Demand Small Medium Large Very large Good $50 $80 $100 $300 Fair $20 $30 $30 $25 Poor ($10) ($20) ($40 ($160) Average. payoff $20 $30 $30 $55 The best alternative is very large Station.

(e) Minimax Regret Poor $0 Regret Matrix Alternative Demand Small Medium Large Very large Good $250 $220 $200 $0 Fair $10 $0 $0 $5 $10 $30 $150 Max. regret $250 $220 $200 $150 The best alternative is very large Station. (f) Perhaps selecting the alternative of Very large Station is the correct decision as most of the above criteria show this as the best alternative.