.. LTE ED Widget $120,000 $70,000 -$30,000 Hummer 60,000 40,000 20,000 Nimnot 35,000 30,000 30,000 a) Compute the expected value for each decision and select the best one. b) Determine how much the rm would be willing to pay to a market research firm to gain better information about future conditions. Problem # 6 Microcomp is a US. based manufacturer of personal computers. It is planning to build a new manufacturing and distribution facility in eith South Korea, China, Taiwan, the Philippines, or Mexico. It will take approximately 5 years to build the necessary infrastructure (roads, etc.,), construct the new facility, and put it into operation. The eventual cost ofthe facility will differ between countries and will even vary with countries depending on the nancial, labor, and political climate, including monetary exchange rates. The company has estimated the facility cost (in $1,000,0003) in each country under three different future economic and political climates, as follows: Economic/Political Climate Country Decline Same Improve South Korea 21.7 19.1 15.2 China 19.0 18.5 17.6 Taiwan 19.2 17.1 14.9 Philippines 22.5 16.8 13.8 Mexico 25.0 21.2 12.5 A global economist hired by Microcomp, estimates that the probability that the economic and political climate overseas and in Mexico will decline during the next 5 years is 0.4, the probability that it will remain approximately the same is 0.50, and the probability that it will improve is 0.10. 8 uteehonline.utech.edu.jm Private @ .u LTE EB- uuuuuua 1'15th v1 [I'll run; 4. Assume that the bakery (problem 3 above) has obtained the following probability information regarding the demand for pies: P(50) = 0.3, P000) = 0.5, and P(150)= 0.2 3. Which alternative should be chosen using the expected monetary value (EMV) criterion? b. What is the expected value under certainty? c. What is the expected value under perfect information (EVPI)? 5. AAA auto supply store sells rough terrain tires which are ordered every Friday to meet next week's demand. The sales price for the most popular size is $50 per tire and it costs for AAA is $$35. If too many tires are ordered AAA incurs an inventory carrying cost of $2 per tire. lf AAA is out of stock, it forgoes the profits from missed sales. AAA has the option to order 100, 150, or 200 tires to meet next week's demand which can be either 100, 150, or 200 tires. a. Which alternative should be chosen based on the maximax criterion? b. Which alternative should be chosen based on the maximin criterion? c. Which alternative should be chosen based on the Laplace criterio? d. Which alternative should be chosen based on the minimax criterion? 6. Based on its historical demand distribution, assume that AAA Inc has determined the following probability information: P(100) = 0.4 P(150) = 0.3, and P(200) = 0.3 i. Which alternative should be chosen using the expected monetary value (EMV) criterion? ii. What is the expected value under certainty? iii. What is the expected value under perfect information (EVPI)? utechonline.utech.edu.jm G [D [E] II LTE 2. Refer to problem 1. Assume ABC Inc. has hired a marketing research rm that provided additional information regarding next year's demand. Suppose that the probabilities of low and high demand are assessed as follows: P(Low) = 0.4 and P(High) = 0.6. 21. Which alternative should be chosen using the expected monetary value (EMV) criterion? b. What is the expected value under certainty? c. What is the expected value under perfect information (EVPI)? 3. A bakery must decide how many apple-pies to prepare for the upcoming weekend. The bakery has the option to make 50, 100 or 150 apple-pies. Assume that the demand for the pies can be 50, 100, or 150. Each pie costs $5 to make and sells for $7. Unsold pies are donated to a nearby charity centre. Assume that there is no opportunity cost for the lost sales. a. Which alternative should be chosen based on the maximax criterion? b. Which alternative should be chosen based on the maximin criterion? c. Which alternative should be chosen based on the Laplace criterion? d. Which alternative should be chosed based on the minimax regret criterion? 4. Assume that the bakery (problem 3 above) has obtained the following probability information regarding the demand for pies: P(50) = 0.3, P(100) = 0.5, and P(150) = 0.2 a. Which alternative should be chosen using the expected monetary value (EMV) criterion? b. What is the expected value under certainty? c. What is the expected value under perfect information (EVPI)? 5. AAA auto supply store sells rough terrain tires which are ordered every Friday to meet next week's demand. The sales price for the most popular size is $50 per tire and it costs for AAA is $3535. If too many tires are ordered AAA incurs an inventory carrying cost of $2 per tire. lf AAA is out of stock, it forgoes the prots from missed sales. AAA has the option to order 100, 150, or 200 tires to meet next week's demand which can be either 100, 150, or 200 tires. a. Which alternative should be chosen based on the maximax criterion? b. Which alternative should be chosen based on the . . . . ,J 8 utechonline.utech.edu.jm Private @ .Il LTE ED Problem # 4 Maria Rowe is considering the possibility of opening a small dress shop on Fairbanks Avenue, a few blocks from the university. She has located a good mall that attracts Students. Her options are to open a small shop, a medium- sized shop, or no shop at all. The market for a dress shop can be good, average, or bad. The probabilities for these three possibilities are 0.2 for a good market, 0.5 for an average market, and 0.3 for a bad market. The net prot or loss for the medium-sized and small shops for the various market conditions are given in the table below. Building no shop at all yields no loss and no gain. What do you recommend? ALTERNATIVE GOOD MARKET {$3 AVERAGE MARKET BAD MARKET (S) ($) Small Shop 75.000 2.5000 - 40000 Mcdium-sizod Shop 100.000 35000 - 00000 Nosmp \"- Problem # 5 The Big Traders Company is going to introduce one of three new products: a widget, a hummer, or a nimnot. The market conditions (favourble, stable, or unfavourable) will determine the prot or loss the company realizes, as shown in the following payoff table: Market Conditions Favorable Stable Unfavorable Product .2 .7 . ] Widget $120,000 $70,000 -$3 0,000 Hummer 60,000 40,000 20,000 Nimnot 3 5,000 30,000 30,000 8 utechonline.utech.edu.jm Private 12:11 LTE Taiwan 19.2 17.1 14.9 Philippines 22.5 16.8 13.8 Mexico 25.0 21.2 12.5 A global economist hired by Microcomp, estimates that the probability that the economic and political climate overseas and in Mexico will decline during the next 5 years is 0.4, the probability that it will remain approximately the same is 0.50, and the probability that it will improve is 0.10. Determine: a) The best country to construct the new facility in and b) The expected value of perfect information Problem #7 a) Use the Expected Money Value approach to determine the optimal decision based on the information below. STATE OF NATURE Decision Alternative S, S, S3 d 25 19 -2.0 d 10 16 -8.5 The decision maker has obtained the probability assessments: P( S, ) = 0.65, P( S2) = 0.15 and P( S3 ) = 0.20. b) Use the data above to calculate the Expected Value of Perfect Information. Problem #8 Consider the pay-off table below. Assume that the following probabilities are specified for the states of nature. P(1) = 0.1 ; P(2) = 0.4; and P(3) = 0.3 . - STATE OF NATURE DECISION S S2 S 3 SA d 35 21 25 12 27 25 20 18 D 22 26 21 28 d4 20 25 28 33 utechonline.utech.edu.jm - PrivateIII LTE + ' Trade Bill Crop Pass Fail Corn $35 ,000 $ 8,000 Peanuts 18,000 12,000 Red Peas 22,000 20,000 Determine the best crop to plant, using the following information: a) Maximax b) Maximin e) Minimax Regret d) Equal likelihood Problem # 3. A local real estate investor in Montego Bay is considering three alternative investments: a guesthouse, a restaurant, or a night club. Prots from the guest house or restaurant will be affected by the availability of gasoline and the number of tourists; prots from the night club will be relatively stable under any conditions. The following table shows the prot or loss that could result from each investment: Gasoline Availability Investment Shortage Stable Supply Sumlus Guest house -$8,000 $15,000 $20,000 Restaurant 2,000 8,000 5,000 Night Club 6,000 6,000 5,000 Determine the best investment, using the following decision criteria. a) Maximax b) Maximin c) Minimax Regret d) Equally Likely Problem # 4 8 utechonline.utech.edu.jm Private m at LTE EB- UNIVERSITY OF TECHNOLOGY JAMAICA FACULTY OF BUSINESS AND MANAGEMENT SCHOOL OF BUSINESS ADMINISTRATION DECISION SCIENCE lULORIAL WDRKSHEET DECISION ANALYSIS Problem # 1 T. Bone Puckett, has acquired a textile company on Marcus Garvey Drive and is considering the capacity of the plant to satisfy future orders. Given the following conditional value table, determine the appropriate decision under uncertainty i.e., the decision maker does not know the probability of the outcomes using a) Maximax b) Maximin c) Laplace (Equally Likely) d) Minimax Regret States of Nature Very Favorable Average Unfavorable Alternatives Market Market Market Build new plant $350,000 $240,000 -$3 00,000 Subcontract $ 1 80,000 $ 90,000 -$ 20,000 Overtime $110,000 $ 60,000 -$ 10,000 Do nothing $ 0 $ 0 $ 0 Problem #2 A Farmer in St. Elizabeth must decide which crop to plant next year on his land: corn, peanuts, or red peas. The return from each crop will be determined by whether a new trade bill with CARICOM is passed in Parliament. The prot the farmer will realize from each crop, given the two possible results on the trade bill is shown in the following payoff table: utechonline.utech.edu.jm C); G [D [E] 12:12 LTE C Value of Perfect Information. Problem #8 Consider the pay-off table below. Assume that the following probabilities are specified for the states of nature. P(1) = 0.1 ; P(2) = 0.4; and P(3) = 0.3. - STATE OF NATURE DECISION S S2 S3 SA d1 35 21 25 12 d2 27 25 20 18 D3 22 26 21 28 d4 20 25 28 33 a. Find the decision that maximizes the expected net dollar return. b. Find the decision that minimizes the expected net dollar return. c. Use the data above to calculate the Expected Value of Perfect Information. EXCEL PROBLEMS 1. Abc Inc. must make a decision on its current capacity for next year. Estimated profits (in $000's) based on next year's demand are shown in the table below. Next Year's Demand Alternative Low High Expand $100 $200 Subcontract $50 $120 Do Nothing $40 $50 a. Which alternative should be chosen based on the maximax criterion? b. Which alternative should be chosen based on the maximin criterion? c. Which alternative should be chosen based on the Laplace criterion? d. Which alternative should be chosen based on the minimax regret criterion A utechonline.utech.edu.jm - Private