Decision Investment Motel Restaurant Theater Shortage -$7,500 $3,000 $5,000 States of Nature Gasoline Availablity Stable Supply $12,000 $7,000 $6,000 Surplus $23,000 $6,500 $4,000 Maximum Minimum $23,000 -$7,500 $7,000 $3,000 $6,000 $4,000 Maximax decision = Maximin decision = Regret Table Decision Investment Motel Restaurant Theater States of Nature Gasoline Availablity Shortage Stable Supply Surplus $12,500 $0 $0 $2,000 $5,000 $16,500 $0 $6,000 $19,000 Minimax regret = Hurwicz alpha = 1 - alpha = Motel Restaurant Theater 0.3 0.7 $1,650 $4,200 $4,600 Decision: $9,167 $5,500 $5,000 Decision: Equal Likelihood Motel Restaurant Theater Maximum $12,500 $16,500 $19,000 Summary a) maximax b) maximin c) minimax regret d) Hurwicz (alpha = 0.4) e) Equal Likelihood Decision Motel Theater Motel or Restaurant Theater Motel Decision Tables Data Profit Probability Sun Visors Umbrellas Rain Overcast Sunshine 0.35 0.25 0.4 -400 2100 -200 0 1500 -800 Opportunity Loss Table Rain Overcast Probability 0.35 0.25 Sun Visors 2500 200 Umbrellas 0 0 Sunshine 0.4 0 EV Sun Visor Umbrella EOL Sun Visor Umbrella 2300 Decision: Minimize your Expected Opportunity Loss Real estate Development Decision Tables Interest Rate Project Decline (0.45) Stable (0.35) Increase (0.2) Office park $0.40 $1.55 $3.50 Office park Office building 2.5 1.8 2.75 Office building Warehouse 1.7 1.45 1.5 Warehouse Mall 0.8 2.3 3.7 Mall Condominiums 3.2 1.5 0.5 Condominiums Opportunity Loss table Interest Rate Project Decline (0.45) Office park Office building Warehouse Mall Condominiums EVPI Stable (0.35) Increase (0.2) EV Decision Economic Conditions Degree Program Graphic design Nursing Real estate Medical technology Culinary technology Computer information technology Recession 150,000 160,000 125,000 135,000 110,000 130,000 Average 175,000 180,000 165,000 180,000 145,000 150,000 Good 220,000 205,000 220,000 210,000 235,000 190,000 Robust 200,000 215,000 210,000 270,000 205,000 245,000 Maximum Minimum 220,000 150,000 215,000 160,000 220,000 125,000 270,000 135,000 235,000 245,000 110,000 130,000 MAX MIN Maximax decision = Maximin decision = Regret Table Economic Conditions Degree Program Graphic design Nursing Real estate Medical technology Culinary technology Computer information technology Recession 10,000 0 35,000 25,000 50,000 Average 5,000 0 15,000 0 35,000 Good 15,000 30,000 15,000 25,000 0 Robust 70,000 55,000 60,000 0 65,000 30,000 30,000 45,000 25,000 Decision: Decision: Maximax Maximin Equal Likelihood Graphic design Nursing Real estate Medical technology Culinary technology Computer information technology $186,250 $190,000 $180,000 $198,750 $173,750 $178,750 Decision: Hurwicz alpha = 1 - alpha = Graphic design Nursing Real estate Medical technology Culinary technology Computer information technology 0.4 0.6 $178,000 $182,000 $163,000 $189,000 $160,000 $176,000 Decision: 0 0 Summary a) maximax b) maximin c) equal likelihood d) Hurwicz (alpha = 0.5) Decision Real estate Nursing Real estate Real estate 0.7 Shortage 250000 Compact Cars 250000 0.3 Surplus 150000 150000 Problem #25 (reference) Data Profit Shortage Probability 0.7 Compact cars 250000 Full-sized cars -90000 Trucks 125000 0.7 Shortage -90000 Full-sized cars -90000 1 0 0.3 Surplus Decision 650000 650000 0.7 Shortage 125000 Trucks 125000 0.3 Surplus 180000 170000 180000 Surplus 0.3 150000 650000 180000 Results EMV ID Name Value 0 TreePlan 1 2 3 4 5 6 7 8 9 Prob 0 0 0 0 0 Pred Kind 0D 0E 0E 0E 1T 1T 2T 2T 3T 3T NS S1 3 2 2 2 0 0 0 0 0 0 S2 1 4 6 8 0 0 0 0 0 0 S3 2 5 7 9 0 0 0 0 0 0 S4 3 0 0 0 0 0 0 0 0 0 S5 0 0 0 0 0 0 0 0 0 0 Row 0 0 0 0 0 0 0 0 0 0 Col 14 4 14 24 2 7 12 17 22 27 Mark 1 5 5 5 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 MAT540 Homework Week 2 Page 1 of 4 MAT540 Week 2 Homework Chapter 12 1. A local real estate investor in Orlando is considering three alternative investments; a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment: Weather Conditions Investment Shortage Stable Supply Surplus $-7,500 $12,000 $23,000 Restaurant 3000 7,000 6,500 Theater 5000 6,000 4,000 Motel Determine the best investment, using the following decision criteria. a. Maximax b. Maximin c. Minimax regret d. Hurwicz ( = 0.4) e. Equal likelihood 2. A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 35% chance of rain, a 25% chance of overcast skies, and a 40% chance of sunshine, according to the weather forecast in college junction, where the game is to be held. The manager estimates that the following profits will result from each decision, given each set of weather conditions: MAT540 Homework Week 2 Page 2 of 4 Weather Conditions Decision Rain Overcast Sunshine 0.35 0.25 0.40 Sun visors $-400 $-200 $1,500 Umbrellas 2,100 0 -800 a. Compute the expected value for each decision and select the best one. b. Develop the opportunity loss table and compute the expected opportunity loss for each decision. 3. Place-Plus, a real estate development firm, is considering several alternative development projects. These include building and leasing an office park, purchasing a parcel of land and building an office building to rent, buying and leasing a warehouse, building a strip mall, and selling condominiums. The financial success of these projects depends on interest rate movement in the next 5 years. The various development projects and their 5- year financial return (in $1,000,000s) given that interest rates will decline, remain stable, or increase, are in the following payoff table. Place-Plus real estate development firm has hired an economist to assign a probability to each direction interest rates may take over the next 5 years. The economist has determined that there is a 0.45 probability that interest rates will decline, a 0.35 probability that rates will remain stable, and a 0.2 probability that rates will increase. a. Using expected value, determine the best project. b. Determine the expected value of perfect information. Interest Rate Project Decline Stable Increase Office park $0.4 $1.55 $3.5 Office building 2.5 1.8 2.75 Warehouse 1.7 1.45 1.5 Mall 0.8 2.3 3.5 Condominiums 3.2 1.5 0.5 MAT540 Homework Week 2 Page 3 of 4 4. The director of career advising at Orange Community College wants to use decision analysis to provide information to help students decide which 2-year degree program they should pursue. The director has set up the following payoff table for six of the most popular and successful degree programs at OCC that shows the estimated 5-Year gross income ($) from each degree for four future economic conditions: Economic Conditions Degree Program Recession Average Good Robust Graphic design 150,000 175,000 220,000 200,000 Nursing 160,000 180,000 205,000 215,000 Real estate 125,000 165,000 220,000 210,000 Medical technology 135,000 180,000 210,000 270,000 Culinary technology 110,000 145,000 235,000 205,000 Computer information 130,000 150,000 190,000 245,000 technology Determine the best degree program in terms of projected income, using the following decision criteria: a. Maximax b. Maximin c. Equal likelihood d. Hurwicz (=0.4) 5. Construct a decision tree for the following decision situation and indicate the best decision. Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership. They have three offers: from a foreign compact car company, from a U.S. producer of full-sized cars, and from a truck company. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years. The profit from each type of dealership, given the availability of gas, is shown in the following payoff table: MAT540 Homework Week 2 Page 4 of 4 Gasoline Availability Dealership Shortage Surplus 0.7 0.3 Compact cars $25,000 $150,000 Full-sized cars -90,000 650,000 Trucks 125,000 170,000 Decision Tree diagram to complete: Shortage 0.7 $250,000 2 Compact cars 1 Full-sized cars Surplus 0.3 $150,00 0 Shortage 0.7 -$90,000 3 $650,000 Surplus 0.3 Trucks Shortage 0.7 $125,000 Surplus 0.3 $170,000 4