Question

5.19 The management of Dream Cruises, Ltd., operating in the Caribbean, has established the need for expanding its fleet capacity and is considering what the best plan for the next 8-year planning period will be. One strategy is to buy a larger 40,000-ton cruise ship now, which would be most profitable if demand is high. Another strategy would be to start with a small 15,000-ton ship now and consider buying another medium 25,000-ton ship 3 years later. The planning department has estimated the probabilities for high and low demand r each period to be 0.6 and 0.4. If the company buys the large ship, then the annual profit after taxes for the next 8 years is estimated to be $800,000 if demand is high and $100,000 if it is low. If the company buys the small ship, then the annual profits each year will be $300,000 if demand is high and $150,000 if it is low. After 3 years with the small vessel, a decision for new capacity will be reviewed. At this time the firm may decide to expand by adding a 25,000-ton ship or by continuing with the small one. The annual profit after expansion will be $700,000 if demand is high and $120,000 if it is low. a. Prepare a decision tree that shows the actions available, the states of nature, and the annual profits. b. Calculate the total expected profit for each branch in the decision tree covering 8 years of operation. c. Determine the optimum fleet-expansion strategy for Dream Cruises, Ltd.

Answer 1

Answer: - = 6400,000 Pleigh) = 0.6 800,000+ 8 Buy Large Ship 100,000x8 = 800,000 IP (Low) 204 P(High) = 0.6 300,000 X 3+ 700,000 X5 = 44.00000 Buy medium ship Buy Small Pllow = 0.4 150000 x 34/2000 15 = 165000 P(High) = 0.6 300,000 X 8 - 9400,000 ship Continue with Small Ship P (Low) = 0.4 150,000x8 = 1200,000

b. expected value at node 4 = 0.6*(300000*8)+0.4*(150000*8) = 1920000

Expected value at node 3 = 0.6*(300000*3+700000*5)+0.4*(150000*3+120000*5) = 3060000

Expected value at node 2 = max(1920000,3060000) = 3060000

Expected value at node 1 = 0.6*(800000*8)+0.4*(100000*8) = 4160000

c.

Optimum fleet-expansion strategy is to buy large ship as expected value of buying large ship = Expected value at node 1 = 4160000 is higher than expected value of buying small ship = Expected value at node 2 = 3060000