Textbook: pp Chapter 3: Decision Analysis

Size: px
Start display at page:

Download "Textbook: pp Chapter 3: Decision Analysis"

Transcription

1 1 Textbook: pp Chapter 3: Decision Analysis

2 2 Learning Objectives After completing this chapter, students will be able to: List the steps of the decision-making process. Describe the types of decision-making environments. Make decisions under uncertainty. Use probability values to make decisions under risk. Use computers to solve basic decision-making problems. Develop accurate and useful decision trees. Revise probabilities using Bayesian analysis. Understand the importance and use of utility theory in decision making.

3 3 Introduction 雷军 What is involved in making a good decision? 2015 Decision theory is an analytic and systematic approach to the study of decision making A good decision is one that is based on logic, considers all available data and possible alternatives, and applies a quantitative approach

4 4 The Six Steps in Decision Making 1. Clearly define the problem at hand 2. List the possible alternatives 3. Identify the possible outcomes or states of nature 4. List the payoff (typically profit) of each combination of alternatives and outcomes 5. Select one of the mathematical decision theory models 6. Apply the model and make your decision

5 5 Thompson Lumber Company (1 of 3) Step 1 Define the problem Consider expanding by manufacturing and marketing a new product backyard storage sheds Step 2 List alternatives Construct a large new plant Construct a small new plant Do not develop the new product line Step 3 Identify possible outcomes, states of nature The market could be favourable or unfavourable

6 6 Thompson Lumber Company (2 of 3) Step 4 List the payoffs Identify conditional values for the profits for large plant, small plant, and no development for the two possible market conditions ( NEXT SLIDE) Step 5 Select the decision model Depends on the environment and amount of risk and uncertainty Step 6 Apply the model to the data

7 7 Thompson Lumber Company (3 of 3) Decision Table with Conditional Values for Thompson Lumber Note: It is important to include all alternatives, including do nothing.

8 8 Types of Decision-Making Environments Decision making under certainty o The decision maker knows with certainty the consequences of every alternative or decision choice Decision making under uncertainty o The decision maker does not know the probabilities of the various outcomes Decision making under risk o The decision maker knows the probabilities of the various outcomes

9 9 Decision Making Under Uncertainty Several states of nature exist and a manager cannot assess the outcome probability with confidence or when virtually no probability data are available: Criteria for making decisions under uncertainty: 1. Maximax (optimistic) Profit 2. Maximin (pessimistic) 3. Criterion of realism (Hurwicz) 4. Equally likely (Laplace) Cost 5. Minimax regret

10 10 Optimistic Used to find the alternative that maximises the maximum payoff maximax criterion o Locate the maximum payoff for each alternative o Select the alternative with the maximum number Thompson s Maximax Decision

11 11 Pessimistic Used to find the alternative that maximises the minimum payoff maximin criterion Locate the minimum payoff for each alternative Select the alternative with the maximum number Thompson s Maximin Decision

12 The advantage of this approach is that it allows the decision maker to build in personal feelings about relative optimism and pessimism!!! 12 Criterion of Realism (Hurwicz) (1 of 2) Often called weighted average Compromise between optimism and pessimism Select a coefficient of realism α, with 0 α 1 α = 1 is perfectly optimistic α = 0 is perfectly pessimistic Compute the weighted averages for each alternative Select the alternative with the highest value Weighted average = α(best in row) + (1 α)(worst in row)

13 13 Weighted average = α(best in row) + (1 α)(worst in row) Criterion of Realism (Hurwicz) (2 of 2) For the large plant alternative using α = 0.8 (0.8)(200,000) + (1 0.8)( 180,000) = 124,000 For the small plant alternative using α = 0.8 (0.8)(100,000) + (1 0.8)( 20,000) = 76,000 Thompson s Criterion of Realism Decision

14 14 Equally Likely (Laplace) Considers all the payoffs for each alternative o Find the average payoff for each alternative o Select the alternative with the highest average Thompson s Equally Likely Decision: 200,000 * (-180,000) * 0.5 =

15 15 Minimax Regret (1 of 4) Based on opportunity loss or regret o The difference between the optimal profit and actual payoff for a decision 1. Create an opportunity loss table by determining the opportunity loss from not choosing the best alternative 2. Calculate opportunity loss by subtracting each payoff in the column from the best payoff in the column 3. Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number

16 16 Minimax Regret (2 of 4) Determining Opportunity Losses for Thompson Lumber:

17 17 Minimax Regret (3 of 4) Opportunity Loss Table for Thompson Lumber:

18 18 Minimax Regret (4 of 4) Thompson s Minimax Decision Using Opportunity Loss:

19 19 Decision Making Under Risk (1 of 2) When there are several possible states of nature and the probabilities associated with each possible state are known where o Most popular method choose the alternative with the highest expected monetary value (EMV) X i = payoff for the alternative in state of nature i P(X i ) = EMV alternative = X P X i i probability of achieving payoff X i (i.e., probability of state of nature i) = summation symbol

20 20 Decision Making Under Risk (2 of 2) Expanding the equation: EMV (alternative i) = (payoff of first state of nature) (probability of first state of nature) + (payoff of second state of nature) (probability of second state of nature) + + (payoff of last state of nature) (probability of last state of nature)

21 21 EMV for Thompson Lumber (1 of 2) Each market outcome has a probability of occurrence of 0.50 Which alternative would give the highest EMV? EMV (large plant) EMV (small plant) = ($200,000)(0.5) + ( $180,000)(0.5) = $10,000 = ($100,000)(0.5) + ( $20,000)(0.5) = $40,000 EMV (do nothing) = ($0)(0.5) + ($0)(0.5) = $0 EMV alternative = X P X i i

22 22 EMV for Thompson Lumber (2 of 2) Decision Table with Probabilities and EMVs for Thompson Lumber:

23 23 Expected Value of Perfect Information (EVPI) (1 of 5) Mr. Thompson has been approached by Scientific Marketing (SM), a firm that proposes to help him make the decision about whether to build the plant to produce storage sheds. SM claims that its technical analysis will tell Mr. Thompson with certainty whether the market is favourable for his proposed product (environment changes from one of decision making under risk to one of decision making under certainty)! This information could prevent Mr. Thompson from making a very expensive mistake. SM would charge Mr. Thompson $65,000 for the information. Should Thompson Lumber purchase the information? Is it worth $65,000 or what would it be worth?

24 24 Expected Value of Perfect Information (EVPI) (2 of 5) EVPI (expected value of perfect information) places an upper bound on what you should pay for additional information EVwPI (expected value with perfect information) is the long run average return if we have perfect information before a decision is made EVwPI = (best payoff in state of nature i) (probability of state of nature i)

25 25 Expected Value of Perfect Information (EVPI) (3 of 5) Expanded EVwPI becomes EVwPI = And (best payoff for first state of nature) (probability of first state of nature) + (best payoff for second state of nature) (probability of second state of nature) + + (best payoff for last state of nature) (probability of last state of nature) EVPI = EVwPI Best EMV without perfect information

26 EVwPI = (best payoff in state of nature i) (probability of state of nature i) EVPI = EVwPI Best EMV without perfect information 26 Expected Value of Perfect Information (EVPI) (4 of 5) Decision Table with Perfect Information: Expected Monetary Value

27 27 EVwPI = (best payoff in state of nature i) (probability of state of nature i) EVPI = EVwPI Best EMV without perfect information Expected Value of Perfect Information (EVPI) (5 of 5) The maximum EMV without additional information is $40,000 EVPI = EVwPI Maximum EMV without perfect information = $100,000 $40,000 = $60,000 So the maximum Thompson should pay for the additional information is $60,000. Thompson should not pay $65,000 for this information!

28 28 Expected Opportunity Loss (1 of 2) Expected opportunity loss (EOL) is the cost of not picking the best solution o Construct an opportunity loss table o For each alternative, multiply the opportunity loss by the probability of that loss for each possible outcome and add these together o Minimum EOL will always result in the same decision as maximum EMV o Minimum EOL will always equal EVPI

29 29 Expected Opportunity Loss (2 of 2) EOL (large plant) = (0.50)($0) + (0.50)($180,000) = $90,000 EOL (small plant) = (0.50)($100,000) + (0.50)($20,000) = $60,000 EOL (do nothing) = (0.50)($200,000) + (0.50)($0) = $100,000 EOL Table for Thompson Lumber:

30 30 Sensitivity analysis examines how our decision might change with different input data. Sensitivity Analysis (1 of 4) Define P = probability of a favourable market EMV(large plant) = $200,000P $180,000 (1 P) = $200,000P $180,000 + $180,000P = $380,000P $180,000 EMV(small plant) = $100,000P $20,000 (1 P) = $100,000P $20,000 + $20,000P = $120,000P $20,000 EMV(do nothing) = $0P + 0(1 P) = $0

31 EMV(large plant) = $380,000P $180,000 EMV(small plant) = $120,000P $20,000 EMV(do nothing) = $0 31 Sensitivity Analysis (2 of 4)

32 EMV(large plant) = $380,000P $180,000 EMV(small plant) = $120,000P $20,000 EMV(do nothing) = $0 32 Sensitivity Analysis (3 of 4) Point 1: EMV(do nothing) = EMV(small plant) Point 2: EMV(small plant) = EMV(large plant)

33 Sensitivity Analysis (4 of 4) 33

34 34 A Minimisation Example (1 of 10) The following example illustrates how the decision-making criteria are applied to problems in which the payoffs are costs that should be minimised. The Business Analytics department of Henan University of Technology will be signing a 3-year lease for a new copy machine, and three different machines are being considered! For each of these, there is a monthly fee, which includes service on the machine, plus a charge for each copy. The number of copies that would be made each month is uncertain, but the department has estimated that the number of copies per month could be 10,000 or 20,000 or 30,000.

35 35 A Minimisation Example (2 of 10) Payoff Table with Monthly Copy Costs for Business Analytics Department: Which machine should be selected?

36 36 A Minimisation Example (3 of 10) Best and Worst Payoffs (Costs) for Business Analytics Department: If the decision maker is optimistic, only the best (minimum) payoff for each decision is considered. The BEST (minimum) of these is 700. Thus machine C would be selected. If the decision maker is pessimistic, only the worst (maximum) payoff for each decision is considered and the BEST of these is 1,150. Thus machine A would be selected.

37 37 A Minimisation Example (4 of 10) Our assumption! Using Hurwicz criteria with 70% coefficient of realism Weighted average = 0.7(best payoff) + (1 0.7)(worst payoff) For each machine: Machine A: 0.7(950) + 0.3(1,150) = 1,010 Machine B: 0.7(850) + 0.3(1,350) = 1,000 Machine C: 0.7(700) + 0.3(1,300) = 880 The decision would be to select Machine C because it has the lowest weighted average cost!

38 38 A Minimisation Example (5 of 10) For equally likely criteria Average payoff for each machine: Machine A: ( , ,150) 3 = 1,050 Machine B: ( , ,350) 3 = 1,100 Machine C: ( , ,300) 3 = 1,000 Based on the equally likely criterion: Machine C would be selected because it has the lowest average cost!

39 39 A Minimisation Example (6 of 10) For EMV criteria probabilities must be known for each state of nature: State of nature 1: State of nature 2: State of nature 3: We can now use these probabilities to calculate the EMVs!

40 40 A Minimisation Example (7 of 10) For EMV criteria EMV alternative = X P X i i Expected Monetary Values and Expected Values with Perfect Information for Business Analytics Department: Machine C would be selected because it has the lowest EMV!

41 Perfect information would lower the expected value by $45! 41 EVwPI = (best payoff in state of nature i) (probability of state of nature i) EVPI = EVwPI Best EMV without perfect information A Minimisation Example (8 of 10) For EMV criteria To find the EVPI, we first find the payoffs (costs) that would be experienced with perfect information! The best payoff in each state of nature is the lowest value (cost) in the state of nature! EVwPI = $700*0.4 + $1,000*0,3 + $1,150*0.3 = $925 Best EMV without perfect information = $970 EVPI = $970 $925 = $45

42 42 A Minimisation Example (9 of 10) Opportunity loss criteria We must first develop the opportunity loss table: In each state of nature, the opportunity loss indicates how much worse each payoff is than the best possible payoff in that state of nature! The best payoff would be the lowest cost! We subtract the lowest value in each column from all the values in that column!

43 EOL (Machine A) = 0.4* * *0 = 115 EOL (Machine B) = 0.4* * *200 = 150 EOL (Machine C) = 0.4* * *150 = A Minimisation Example (10 of 10) Opportunity loss criteria We must first develop the opportunity loss table: Once the opportunity loss table has been developed, the minimax regret criterion is applied! The maximum regret for each alternative is found, and the alternative with the minimum of these maximums is selected! We select Machine C! The probabilities are used to compute the expected opportunity losses! Machine C has the lowest EOL of $45, so it would be selected based on the minimum EOL criterion!

44 44 PROGRAMME 3.1A Use File: 3.3.dec Using Software (1 of 3) QM for Windows Input for Thompson Lumber Example: Step 1 Step 2 Step 3

45 45 PROGRAMME 3.1B Using Software (2 of 3) QM for Windows Input for Thompson Lumber Example: Enter data into table and type the row and column names

46 46 PROGRAMME 3.1C Using Software (3 of 3) QM for Windows Output Screen for Thompson Lumber Example: Click Window to see more information (e.g. EVPI and opportunity loss results)

47 47 PROGRAMME 3.2A Using Excel 2016 (1 of 3) Excel QM Results for Thompson Lumber Example: Please open the Excel QM v5.2 file on your desktop!

48 48 PROGRAMME 3.2A Using Excel 2016 (2 of 3) Excel QM Results for Thompson Lumber Example: To see the formulas, hold down the control key (Ctrl) and press the (grave accent) key

49 49 PROGRAMME 3.2B Using Excel 2016 (3 of 3) Key Formulas in Excel QM for Thompson Lumber Example:

50 50 Decision Trees Any problem that can be presented in a decision table can be graphically represented in a decision tree o All decision trees contain decision points/nodes and state-of-nature points/nodes At decision nodes one of several alternatives may be chosen At state-of-nature nodes one state of nature will occur o Most beneficial when a sequence of decisions must be made!

51 51 Structure of Decision Trees Trees start from left to right Trees represent decisions and outcomes in sequential order Squares represent decision nodes Circles represent states of nature nodes Lines or branches connect the decisions nodes and the states of nature

52 52 Five Steps of Decision Tree Analysis 1. Define the problem 2. Structure or draw the decision tree 3. Assign probabilities to the states of nature 4. Estimate payoffs for each possible combination of alternatives and states of nature 5. Solve the problem by computing expected monetary values (EMVs) for each state of nature node

53 At decision nodes one of several alternatives may be chosen! At state-of-nature nodes one state of nature will occur! 53 Thompson s Decision Tree (1 of 2)

54 54 Thompson s Decision Tree (2 of 2) Completed and Solved Decision Tree for Thompson Lumber: The branch leaving the decision node leading to the stateof-nature node with the highest EMV should be chosen. A small plant should be built!

55 55 Thompson s Complex Decision Tree (1 of 6) - sequential decisions need to be made - Let s say that Mr. Thompson has two decisions to make, with the second decision dependent on the outcome of the first. Before deciding about building a new plant, Mr. Thompson has the option of conducting his own marketing research survey, at a cost of $10,000. The information from his survey could help him decide whether to construct a large plant, a small plant, or not to build at all. Mr. Thompson recognises that such a market survey will not provide him with perfect information, but it may help quite a bit nevertheless.

56 At decision nodes one of several alternatives may be chosen! At state-of-nature nodes one state of nature will occur! 56 Thompson s Complex Decision Tree (2 of 6) Larger Decision Tree with Payoffs and Probabilities for Thompson Lumber:

57 57 Thompson s Complex Decision Tree (3 of 6) 1. Given favourable survey results EMV alternative = X P X i i EMV(node 2) = EMV(large plant positive survey) = (0.78)($190,000) + (0.22)( $190,000) = $106,400 EMV(node 3) = EMV(small plant positive survey) = (0.78)($90,000) + (0.22)( $30,000) = $63,600 EMV for no plant = $10,000 If the survey results are favourable, a large plant should be built!

58 58 Thompson s Complex Decision Tree (4 of 6) 2. Given negative survey results EMV(node 4) = EMV(large plant negative survey) = (0.27)($190,000) + (0.73)( $190,000) = $87,400 EMV(node 5) = EMV(small plant negative survey) = (0.27)($90,000) + (0.73)( $30,000) = $2,400 EMV for no plant = $10,000 Given a negative survey result a small plant should be built!

59 59 Thompson s Complex Decision Tree (5 of 6) 3. Expected value of the market survey EMV(node 1) = EMV(conduct survey) = (0.45)($106,400) + (0.55)($2,400) = $47,880 + $1,320 = $49, Expected value no market survey EMV(node 6) EMV(node 7) = EMV(large plant) = (0.50)($200,000) + (0.50)( $180,000) = $10,000 = EMV(small plant) = (0.50)($100,000) + (0.50)( $20,000) = $40,000 Building a small plant is the best choice, given that the marketing research is not performed. EMV for no plant = $0

60 60 Thompson s Complex Decision Tree (6 of 6) Thompson s Decision Tree with EMVs Shown: We move back to the first decision node and choose the best alternative: The expected monetary value of conducting the survey is $49,200, versus an EMV of $40,000 for not conducting the study, so the best choice is to seek marketing information. If the survey results are favourable we should construct a large plant! But if the research is negative, he should construct a small plant!

61 61 Expected Value of Sample Information (1 of 2) Mr. Thompson now realises that conducting the market research is not free! He would like to know what the actual value of doing a survey is! One way of measuring the value of market information is to compute the expected value of sample information (EVSI) which is the increase in expected value resulting from the sample information.

62 62 Expected Value of Sample Information (2 of 2) Thompson wants to know the actual value of doing the survey: where: EVSI = (EV with SI + cost) (EV without SI) EVSI = expected value of sample information EV with SI = expected value with sample information EV without SI = expected value without sample information EVSI = ($49,200 + $10,000) $40,000 = $19,200 Mr Thompson could have paid up to $19,200 for a market study and still come out ahead! Since it costs only $10,000, the survey is indeed worthwhile!

63 EVSI = expected value of sample information EVPI = expected value of perfect information (see Slide 27) 63 Efficiency of Sample Information Possibly many types of sample information available Different sources can be evaluated EVSI Efficiency of sample information = 100% EVPI For Thompson 19,200 Efficiency of sample information = 100% = 32% 60,000 Market survey is only 32% as efficient as perfect information!

64 64 Sensitivity Analysis (1 of 2) How sensitive are the decisions to changes in the probabilities? Thompson Lumber Example: How sensitive is our decision (to conduct the marketing survey) to the probability of a favourable survey result? If the probability of a favourable result (p =.45) were to change, would we make the same decision? How much could it change before we would make a different decision?

65 65 Sensitivity Analysis (2 of 2) p = probability of a favourable survey result (1 p) = probability of a negative survey result EMV alternative = X P X i i EMV(node 1) = ($106,400)p +($2,400)(1 p) = = $104,000p + $2,400 We are indifferent when the EMV of node 1 is the same as the EMV of not conducting the survey $104,000p + $2,400 = $40,000 $104,000p = $37,600 p = $37,600 $104,000 = 0.36 If p < 0.36, do not conduct the survey If p > 0.36, conduct the survey

66 Thompson s Complex Decision Tree 66

67 67 Bayesian Analysis Many ways of getting probability data o Management s experience and intuition o Historical data o Computed from other data using Bayes theorem Bayes theorem incorporates initial estimates and information about the accuracy of the sources (e.g. market research survey) Bayes theorem approach recognises that a decision maker does not know with certainty what state of nature will occur. It allows the manager to revise his/her prior probability assessments based on new information

68 * Mr. Thompson s best estimates of a favourable and unfavourable market without any market survey information! 68 Calculating Revised Probabilities (1 of 9) In the Thompson Lumber case we made the assumption that the four conditional probabilities were known: P(favourable market(fm) survey results positive) = 0.78 P(unfavourable market(um) survey results positive) = 0.22 P(favourable market(fm) survey results negative) = 0.27 P(unfavourable market(um) survey results negative) = 0.73 Prior probabilities*: P(FM) = 0.50 P(UM) = 0.50

69 69 Calculating Revised Probabilities (2 of 9) Let s see how Mr. Thompson was able to derive these values with Bayes theorem: From discussions with market research specialists, Mr. Thompson knows that special surveys can either be positive (predict a favourable market) or be negative (predict an unfavourable market). The experts have told Mr. Thompson that, statistically, of all new products with a favourable market (FM), market surveys were positive and predicted success correctly 70% of the time. Thirty percent of the time the surveys falsely predicted negative results or an unfavourable market (UM). When there was actually an unfavourable market for a new product, 80% of the surveys correctly predicted negative results. The surveys incorrectly predicted positive results the remaining 20% of the time.

70 70 Calculating Revised Probabilities (3 of 9) Market Survey Reliability in Predicting States of Nature: They are an indication of the accuracy of the survey to be conducted!

71 71 Calculating Revised Probabilities (4 of 9) Let s compute Thompson s posterior probabilities: We need the probability of a favourable or unfavourable market given a positive or negative result from the market study! General form of Bayes theorem (see Chapter 2): P( A B) P( B A) P( A) P( B A) P( A) P( B A ) P( A ) Where A, B = any two events A = complement of A A = favourable market B = positive survey

72 72 Calculating Revised Probabilities (5 of 9) P(FM survey positive) = P(survey positive FM) P(FM) P (survey positive FM) P(FM) P(survey positive UM) P(UM) (0.70)(0.50) (0.70)(0.50)+(0.20)(0.50) 0.45 P(UM survey positive) = = = P(survey positive UM)P(UM) P(survey positive UM)P(UM) + P(survey positive FM)P(FM) (0.20)(0.50) (0.20)(0.50)+(0.70)(0.50) = = 0.22 probability of a positive survey

73 Alternative method for these calculations is to use a probability table! 73 Calculating Revised Probabilities (6 of 9) Probability Revisions Given a Positive Survey:

74 74 Calculating Revised Probabilities (7 of 9) P(FM survey negative) P(survey negative FM) P(FM) P (survey negative FM) P(FM) P (survey negative UM) P(UM) (0.30)(0.50) (0.30)(0.50)+(0.80)(0.50) 0.55 P(UM survey negative) P(survey negative UM) P(UM) P (survey negative UM) P(UM) P(survey negative FM) P(FM) (0.80)(0.50) (0.80)(0.50)+(0.30)(0.50) 0.55 probability of a negative survey

75 75 Calculating Revised Probabilities (8 of 9) Probability Revisions Given a Negative Survey:

76 76 Calculating Revised Probabilities (9 of 9) The posterior probabilities now provide the Thompson Lumber managers with estimates for each state of nature if the survey results are positive or negative! Mr. Thompson s prior probability of success without a market survey was only Now he is aware that the probability of successfully marketing storage sheds will be 0.78 if his survey shows positive results. His chances of success drop to 27% if the survey report is negative!

77 77 PROGRAMME 3.3A Please open your file QAM_13_Examples Using Excel 2016 (1 of 2) Results of Bayes Calculations in Excel 2016:

78 78 PROGRAMME 3.3B Please open your file QAM_13_Examples Using Excel 2016 (2 of 2) Formulas Used for Bayes Calculations in Excel 2016:

79 79 Potential Problems Using Survey Results We can not always get the necessary data for analysis Survey results may be based only on those cases where an action was taken Conditional probability information may not be as accurate as we would like

80 80 Why do people make decisions that do not maximise their EMV? Utility Theory (1 of 6) Monetary value is not always a true indicator of the overall value of the result of a decision! There are occasions in which people make decisions that would appear to be inconsistent with the EMV criterion! Example: A manager may rule out one potential decision because it could bankrupt the firm if things go bad, even though the expected return for this decision is better than that of all other alternatives!

81 Economists assume that rational people make decisions to maximise their utility! 81 Utility Theory (2 of 6) Why do people make decisions that do not maximise their EMV? The monetary value is not always a true indicator of the overall value of the result of the decision! The overall worth of a particular outcome is called utility, and rational people make decisions that maximise the expected utility! Although at times the monetary value is a good indicator of utility, there are other times when it is not. This is particularly true when some of the values involve an extremely large payoff or an extremely large loss.

82 82 Utility Theory (3 of 6) Example: Suppose that you are the lucky holder of a lottery ticket. Five minutes from now a fair coin could be flipped, and if it comes up tails, you would win $5 million. If it comes up heads, you would win nothing. Just a moment ago a wealthy person offered you $2 million for your ticket. Let s assume that you have no doubts about the validity of the offer. The person will give you a certified check for the full amount, and you are absolutely sure the check would be good.

83 How would you decide? $2 million for sure instead of a 50% chance at nothing? 83 Utility Theory (4 of 6) Your Decision Tree for the Lottery Ticket:

84 84 Utility Theory (5 of 6) Utility assessment assigns the worst outcome a utility of 0 and the best outcome a utility of 1 A standard gamble is used to determine utility values When you are indifferent, your utility values are equal

85 85 Utility Theory (6 of 6) Expected utility of alternative 2 = Expected utility of alternative 1 Utility of other outcome = (p)(utility of best outcome, which is 1) + (1 p)(utility of the worst outcome, which is 0) Utility of other outcome = (p)(1) + (1 p)(0) = p

86 86 A utility curve is a graph that plots utility value versus monetary value! Investment Example (1 of 3) Mrs. Dickson would like to construct a utility curve revealing her preference for money between $0 and $10,000. She can either invest her money in a bank savings account or she can invest the same money in a real estate deal. If the money is invested in the bank, in three years Jane would have $5,000. If she invested in the real estate, after three years she could either have nothing ($0) or $10,000. Mrs. Dickson is very conservative. Unless there is an 80% chance of getting $10,000 from the real estate deal, she would prefer to have her money in the bank. What Mrs. Dickson has done here is to assess her utility for $5,000. When there is an 80% chance (p = 0.8) of getting $10,000, she is indifferent between putting her money in real estate or putting it in the bank. Her utility for $5,000 is thus equal to 0.8, which is the same as the value for p.

87 87 Investment Example (2 of 3) Utility of $5,000

88 88 Investment Example (3 of 3) Let s assess other utility values: Utility for $7,000 = 0.90 Utility for $3,000 = 0.50 Use the three different dollar amounts and assess utilities

89 89 Risk avoider or risk seeker? Utility Curve (1 of 2) Utility Curve for Mrs. Dickson:

90 90 Utility Curve (2 of 2) Typical of a risk avoider o Less utility from greater risk o Avoids situations where high losses might occur o As monetary value increases, utility curve increases at a slower rate A risk seeker gets more utility from greater risk o As monetary value increases, the utility curve increases at a faster rate Someone who is indifferent will have a linear utility curve

91 91 Utility as a Decision-Making Criteria (1 of 5) After a utility curve has been determined, the utility values from the curve are used in making decisions. Monetary outcomes or values are replaced with the appropriate utility values and then decision analysis is performed as usual. The expected utility for each alternative is computed instead of the EMV.

92 92 Utility as a Decision-Making Criteria (2 of 5) Mr. Simkin loves to gamble. He decides to play a game that involves tossing thumbtacks in the air. o If the thumbtack lands point up, he wins $10,000 o If the thumbtack lands point down, he loses $10,000 o Mr. Simkin believes that there is a 45% chance of winning $10,000 and a 55% chance of suffering the $10,000 loss. Alternative 2 is not to gamble. Should Mr. Simkin play the game (alternative 1) or should he not play the game (alternative 2)?

93 EMV (play game) = (0.45)($10,000) + (0.55)( $10,000) = -$1,000 EMV (don t play game) = 0 93 Utility as a Decision-Making Criteria (3 of 5) Decision Facing Mr. Simkin:

94 94 He has a total of $20,000 to gamble, so he has constructed the utility curve based on a best payoff of $20,000 and a worst payoff of a $20,000 loss. Utility as a Decision-Making Criteria (4 of 5) Step 1 Define Mr. Simkin s utilities: U( $10,000) = 0.05 U($0) = 0.15 U($10,000) = 0.30 Utility Curve for Mr. Simkin

95 95 Utility as a Decision-Making Criteria (5 of 5) Step 2 Replace monetary values with utility values E(alternative 1: play the game) =(0.45)(0.30) + (0.55)(0.05) = = E(alternative 2: don t play the game) = 0.15

96 96 Utility as a Decision-Making Criteria (6 of 6) Alternative 1 is the best strategy using utility as the decision criterion. If EMV had been used, alternative 2 would have been the best strategy. The utility curve is a risk-seeker utility curve, and the choice of playing the game certainly reflects this preference for risk!

97 97 Homework --- Chapter 3 End of chapter self-test 1-16 (pp ) Discussion Questions and Problems 3.30 and 3.31 Compile all answers into one document and submit at the beginning of the next lecture! On the top of the document, write your Pinyin-Name and Student ID. Please read Chapter 12!

98 98 Case Study (1 of 8) Starting Right Corporation (p. 125) After watching a movie about a young woman who quit a successful corporate career to start her own baby food company, Julia Day decided that she wanted to do the same. In the movie, the babyfood company was very successful. Julia knew, however, that it is much easier to make a movie about a successful woman starting her own company than to actually do it. The product had to be of the highest quality, and Julia had to get the best people involved to launch the new company. Julia resigned from her job and launched her new company Starting Right.

99 99 Case Study (2 of 8) Julia decided to target the upper end of the baby food market by producing baby food that contained no preservatives but had a great taste. Although the price would be slightly higher than for existing baby food, Julia believed that parents would be willing to pay more for a high-quality baby food. Instead of putting baby food in jars, which would require preservatives to stabilise the food, Julia decided to try a new approach. The baby food would be frozen. This would allow for natural ingredients, no preservatives, and outstanding nutrition.

100 100 Case Study (3 of 8) Getting good people to work for the new company was also important. Julia decided to find people with experience in finance, marketing, and production to get involved with Starting Right. With her enthusiasm and charisma, Julia was able to find such a group. Their first step was to develop prototypes of the new frozen baby food and to perform a small pilot test of the new product. The pilot test received rave reviews.

101 101 Case Study (4 of 8) The final key to getting the young company off to a good start was to raise funds. Three options were considered: corporate bonds, preferred stock, and common stock. Julia decided that each investment should be in blocks of $30,000. Furthermore, each investor should have an annual income of at least $40,000 and a net worth of $100,000 to be eligible to invest in Starting Right. Corporate bonds would return 13% per year for the next 5 years. Julia furthermore guaranteed that investors in the corporate bonds would get at least $20,000 back at the end of five years. Investors in preferred stock should see their initial investment increase by a factor of 4 with a good

102 102 Case Study (5 of 8) market or see the investment worth only half of the initial investment with an unfavourable market. The common stock had the greatest potential. The initial investment was expected to increase by a factor of 8 with a good market, but investors would lose everything if the market was unfavourable. During the next five years, it was expected that inflation would increase by a factor of 4.5% each year.

103 103 Case Study (6 of 8) Discussion Questions 1. Sue Pansky, a retired elementary school teacher, is considering investing in Starting Right. She is very conservative and is a risk avoider. What do you recommend? 2. Ray Cahn, who is currently a commodities broker, is also considering an investment, although he believes that there is only an 11% chance of success. What do you recommend?

104 104 Case Study (7 of 8) Discussion Questions 3. Lila Battle has decided to invest in Starting Right. While she believes that Julia has a good chance of being successful, Lila is a risk avoider and very conservative. What is your advice to Lila? 4. George Yates believes that there is an equally likely chance for success. What is your recommendation? 5. Peter Metarko is extremely optimistic about the market for the new baby food. What is your advice for Pete?

105 105 Case Study (8 of 8) Discussion Questions 6. Julia Day has been told that developing the legal documents for each fundraising alternative is expensive. Julia would like to offer alternatives for both risk-averse and risk-seeking investors. Can Julia delete one of the financial alternatives and still offer investment choices for risk seekers and risk avoiders?

106 106 Multiple Choice Question The following is a payoff table giving costs for various situations. State 1 State 2 State 3 Alternative Alternative Alternative Alternative What decision would an optimist make? A. Alternative 1 B. Alternative 2 C. Alternative 3 D. Alternative 4

107 107 Multiple Choice Question The following is a payoff table giving costs for various situations. State 1 State 2 State 3 Alternative Alternative Alternative Alternative What decision would an pessimist make? A. Alternative 1 B. Alternative 2 C. Alternative 3 D. Alternative 4

108 108 Multiple Choice Question The following is a payoff table giving costs for various situations. State 1 State 2 State 3 Alternative Alternative Alternative Alternative What decision should be made based on the Laplace criterion? A. Alternative 1 B. Alternative 2 C. Alternative 3 D. Alternative 4

109 109 Multiple Choice Question The following is a payoff table giving costs for various situations. State 1 State 2 State 3 Alternative Alternative Alternative Alternative What decision should be made based on the minimax regret criterion? A. Alternative 1 B. Alternative 2 C. Alternative 3 D. Alternative 4

110 110 Multiple Choice Question The following is a payoff table giving costs for various situations. State 1 State 2 State 3 Alternative Alternative Alternative Alternative What are the regret values for Alternative 3 as read from State 1 to State 3? A. 17, 16, 25 B. 29, 0, 7 C. 7, 32, 36 D. 23, 65, 91

111 111 Multiple Choice Question The following is a payoff table giving costs for various situations. State 1 State 2 State 3 Alternative Alternative Alternative Alternative If a person were to use the expected monetary value criterion, what decision would be made? A. Alternative 1 B. Alternative 2 C. Alternative 3 D. Alternative 4

Dr. Abdallah Abdallah Fall Term 2014

Dr. Abdallah Abdallah Fall Term 2014 Quantitative Analysis Dr. Abdallah Abdallah Fall Term 2014 1 Decision analysis Fundamentals of decision theory models Ch. 3 2 Decision theory Decision theory is an analytic and systemic way to tackle problems

More information

Decision Analysis CHAPTER LEARNING OBJECTIVES CHAPTER OUTLINE. After completing this chapter, students will be able to:

Decision Analysis CHAPTER LEARNING OBJECTIVES CHAPTER OUTLINE. After completing this chapter, students will be able to: CHAPTER 3 Decision Analysis LEARNING OBJECTIVES After completing this chapter, students will be able to: 1. List the steps of the decision-making process. 2. Describe the types of decision-making environments.

More information

Chapter 3. Decision Analysis. Learning Objectives

Chapter 3. Decision Analysis. Learning Objectives Chapter 3 Decision Analysis To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Learning Objectives After completing

More information

Introduction LEARNING OBJECTIVES. The Six Steps in Decision Making. Thompson Lumber Company. Thompson Lumber Company

Introduction LEARNING OBJECTIVES. The Six Steps in Decision Making. Thompson Lumber Company. Thompson Lumber Company Valua%on and pricing (November 5, 2013) Lecture 4 Decision making (part 1) Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com LEARNING OBJECTIVES 1. List the steps of the decision-making

More information

Decision Making. DKSharma

Decision Making. DKSharma Decision Making DKSharma Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision making

More information

The Course So Far. Decision Making in Deterministic Domains. Decision Making in Uncertain Domains. Next: Decision Making in Uncertain Domains

The Course So Far. Decision Making in Deterministic Domains. Decision Making in Uncertain Domains. Next: Decision Making in Uncertain Domains The Course So Far Decision Making in Deterministic Domains search planning Decision Making in Uncertain Domains Uncertainty: adversarial Minimax Next: Decision Making in Uncertain Domains Uncertainty:

More information

The Course So Far. Atomic agent: uninformed, informed, local Specific KR languages

The Course So Far. Atomic agent: uninformed, informed, local Specific KR languages The Course So Far Traditional AI: Deterministic single agent domains Atomic agent: uninformed, informed, local Specific KR languages Constraint Satisfaction Logic and Satisfiability STRIPS for Classical

More information

Decision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques

Decision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques 1 Decision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques Thompson Lumber is looking at marketing a new product storage sheds. Mr. Thompson has identified three decision options (alternatives)

More information

Decision Analysis REVISED TEACHING SUGGESTIONS ALTERNATIVE EXAMPLES

Decision Analysis REVISED TEACHING SUGGESTIONS ALTERNATIVE EXAMPLES M03_REND6289_0_IM_C03.QXD 5/7/08 3:48 PM Page 7 3 C H A P T E R Decision Analysis TEACHING SUGGESTIONS Teaching Suggestion 3.: Using the Steps of the Decision-Making Process. The six steps used in decision

More information

Decision Making Models

Decision Making Models Decision Making Models Prof. Yongwon Seo (seoyw@cau.ac.kr) College of Business Administration, CAU Decision Theory Decision theory problems are characterized by the following: A list of alternatives. A

More information

Module 15 July 28, 2014

Module 15 July 28, 2014 Module 15 July 28, 2014 General Approach to Decision Making Many Uses: Capacity Planning Product/Service Design Equipment Selection Location Planning Others Typically Used for Decisions Characterized by

More information

Decision Analysis. Chapter Topics

Decision Analysis. Chapter Topics Decision Analysis Chapter Topics Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility Decision Analysis

More information

Decision Analysis. Chapter Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall

Decision Analysis. Chapter Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Chapter 12 12-1 Chapter Topics Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility

More information

Full file at CHAPTER 3 Decision Analysis

Full file at   CHAPTER 3 Decision Analysis CHAPTER 3 Decision Analysis TRUE/FALSE 3.1 Expected Monetary Value (EMV) is the average or expected monetary outcome of a decision if it can be repeated a large number of times. 3.2 Expected Monetary Value

More information

Chapter 13 Decision Analysis

Chapter 13 Decision Analysis Problem Formulation Chapter 13 Decision Analysis Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information

More information

Decision Analysis. Chapter 12. Chapter Topics. Decision Analysis Components of Decision Making. Decision Analysis Overview

Decision Analysis. Chapter 12. Chapter Topics. Decision Analysis Components of Decision Making. Decision Analysis Overview Chapter Topics Components of Decision Making with Additional Information Chapter 12 Utility 12-1 12-2 Overview Components of Decision Making A state of nature is an actual event that may occur in the future.

More information

SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT. BF360 Operations Research

SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT. BF360 Operations Research SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT BF360 Operations Research Unit 5 Moses Mwale e-mail: moses.mwale@ictar.ac.zm BF360 Operations Research Contents Unit 5: Decision Analysis 3 5.1 Components

More information

DECISION ANALYSIS: INTRODUCTION. Métodos Cuantitativos M. En C. Eduardo Bustos Farias 1

DECISION ANALYSIS: INTRODUCTION. Métodos Cuantitativos M. En C. Eduardo Bustos Farias 1 DECISION ANALYSIS: INTRODUCTION Cuantitativos M. En C. Eduardo Bustos Farias 1 Agenda Decision analysis in general Structuring decision problems Decision making under uncertainty - without probability

More information

1.The 6 steps of the decision process are:

1.The 6 steps of the decision process are: 1.The 6 steps of the decision process are: a. Clearly define the problem Discussion and the factors that Questions influence it. b. Develop specific and measurable objectives. c. Develop a model. d. Evaluate

More information

MBF1413 Quantitative Methods

MBF1413 Quantitative Methods MBF1413 Quantitative Methods Prepared by Dr Khairul Anuar 4: Decision Analysis Part 1 www.notes638.wordpress.com 1. Problem Formulation a. Influence Diagrams b. Payoffs c. Decision Trees Content 2. Decision

More information

Chapter 2 supplement. Decision Analysis

Chapter 2 supplement. Decision Analysis Chapter 2 supplement At the operational level hundreds of decisions are made in order to achieve local outcomes that contribute to the achievement of the company's overall strategic goal. These local outcomes

More information

Decision making under uncertainty

Decision making under uncertainty Decision making under uncertainty 1 Outline 1. Components of decision making 2. Criteria for decision making 3. Utility theory 4. Decision trees 5. Posterior probabilities using Bayes rule 6. The Monty

More information

A B C D E F 1 PAYOFF TABLE 2. States of Nature

A B C D E F 1 PAYOFF TABLE 2. States of Nature Chapter Decision Analysis Problem Formulation Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information Computing

More information

Chapter 12. Decision Analysis

Chapter 12. Decision Analysis Page 1 of 80 Chapter 12. Decision Analysis [Page 514] [Page 515] In the previous chapters dealing with linear programming, models were formulated and solved in order to aid the manager in making a decision.

More information

Agenda. Lecture 2. Decision Analysis. Key Characteristics. Terminology. Structuring Decision Problems

Agenda. Lecture 2. Decision Analysis. Key Characteristics. Terminology. Structuring Decision Problems Agenda Lecture 2 Theory >Introduction to Making > Making Without Probabilities > Making With Probabilities >Expected Value of Perfect Information >Next Class 1 2 Analysis >Techniques used to make decisions

More information

UNIT 5 DECISION MAKING

UNIT 5 DECISION MAKING UNIT 5 DECISION MAKING This unit: UNDER UNCERTAINTY Discusses the techniques to deal with uncertainties 1 INTRODUCTION Few decisions in construction industry are made with certainty. Need to look at: The

More information

Learning Objectives = = where X i is the i t h outcome of a decision, p i is the probability of the i t h

Learning Objectives = = where X i is the i t h outcome of a decision, p i is the probability of the i t h Learning Objectives After reading Chapter 15 and working the problems for Chapter 15 in the textbook and in this Workbook, you should be able to: Distinguish between decision making under uncertainty and

More information

DECISION ANALYSIS. Decision often must be made in uncertain environments. Examples:

DECISION ANALYSIS. Decision often must be made in uncertain environments. Examples: DECISION ANALYSIS Introduction Decision often must be made in uncertain environments. Examples: Manufacturer introducing a new product in the marketplace. Government contractor bidding on a new contract.

More information

Decision Making Supplement A

Decision Making Supplement A Decision Making Supplement A Break-Even Analysis Break-even analysis is used to compare processes by finding the volume at which two different processes have equal total costs. Break-even point is the

More information

Chapter 18 Student Lecture Notes 18-1

Chapter 18 Student Lecture Notes 18-1 Chapter 18 Student Lecture Notes 18-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 18 Introduction to Decision Analysis 5 Prentice-Hall, Inc. Chap 18-1 Chapter Goals After completing

More information

TECHNIQUES FOR DECISION MAKING IN RISKY CONDITIONS

TECHNIQUES FOR DECISION MAKING IN RISKY CONDITIONS RISK AND UNCERTAINTY THREE ALTERNATIVE STATES OF INFORMATION CERTAINTY - where the decision maker is perfectly informed in advance about the outcome of their decisions. For each decision there is only

More information

stake and attain maximum profitability. Therefore, it s judicious to employ the best practices in

stake and attain maximum profitability. Therefore, it s judicious to employ the best practices in 1 2 Success or failure of any undertaking mainly lies with the decisions made in every step of the undertaking. When it comes to business the main goal would be to maximize shareholders stake and attain

More information

Causes of Poor Decisions

Causes of Poor Decisions Lecture 7: Decision Analysis Decision process Decision tree analysis The Decision Process Specify objectives and the criteria for making a choice Develop alternatives Analyze and compare alternatives Select

More information

DECISION MAKING. Decision making under conditions of uncertainty

DECISION MAKING. Decision making under conditions of uncertainty DECISION MAKING Decision making under conditions of uncertainty Set of States of nature: S 1,..., S j,..., S n Set of decision alternatives: d 1,...,d i,...,d m The outcome of the decision C ij depends

More information

Decision Making. D.K.Sharma

Decision Making. D.K.Sharma Decision Making D.K.Sharma 1 Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision

More information

IX. Decision Theory. A. Basic Definitions

IX. Decision Theory. A. Basic Definitions IX. Decision Theory Techniques used to find optimal solutions in situations where a decision maker is faced with several alternatives (Actions) and an uncertain or risk-filled future (Events or States

More information

Subject : Computer Science. Paper: Machine Learning. Module: Decision Theory and Bayesian Decision Theory. Module No: CS/ML/10.

Subject : Computer Science. Paper: Machine Learning. Module: Decision Theory and Bayesian Decision Theory. Module No: CS/ML/10. e-pg Pathshala Subject : Computer Science Paper: Machine Learning Module: Decision Theory and Bayesian Decision Theory Module No: CS/ML/0 Quadrant I e-text Welcome to the e-pg Pathshala Lecture Series

More information

DECISION ANALYSIS. (Hillier & Lieberman Introduction to Operations Research, 8 th edition)

DECISION ANALYSIS. (Hillier & Lieberman Introduction to Operations Research, 8 th edition) DECISION ANALYSIS (Hillier & Lieberman Introduction to Operations Research, 8 th edition) Introduction Decision often must be made in uncertain environments Examples: Manufacturer introducing a new product

More information

Decision Making. BUS 735: Business Decision Making and Research. exercises. Assess what we have learned. 2 Decision Making Without Probabilities

Decision Making. BUS 735: Business Decision Making and Research. exercises. Assess what we have learned. 2 Decision Making Without Probabilities Making BUS 735: Business Making and Research 1 1.1 Goals and Agenda Goals and Agenda Learning Objective Learn how to make decisions with uncertainty, without using probabilities. Practice what we learn.

More information

Objective of Decision Analysis. Determine an optimal decision under uncertain future events

Objective of Decision Analysis. Determine an optimal decision under uncertain future events Decision Analysis Objective of Decision Analysis Determine an optimal decision under uncertain future events Formulation of Decision Problem Clear statement of the problem Identify: The decision alternatives

More information

Johan Oscar Ong, ST, MT

Johan Oscar Ong, ST, MT Decision Analysis Johan Oscar Ong, ST, MT Analytical Decision Making Can Help Managers to: Gain deeper insight into the nature of business relationships Find better ways to assess values in such relationships;

More information

Decision Making. BUS 735: Business Decision Making and Research. Learn how to conduct regression analysis with a dummy independent variable.

Decision Making. BUS 735: Business Decision Making and Research. Learn how to conduct regression analysis with a dummy independent variable. Making BUS 735: Business Making and Research 1 Goals of this section Specific goals: Learn how to conduct regression analysis with a dummy independent variable. Learning objectives: LO5: Be able to use

More information

Next Year s Demand -Alternatives- Low High Do nothing Expand Subcontract 40 70

Next Year s Demand -Alternatives- Low High Do nothing Expand Subcontract 40 70 Lesson 04 Decision Making Solutions Solved Problem #1: see text book Solved Problem #2: see textbook Solved Problem #3: see textbook Solved Problem #6: (costs) see textbook #1: A small building contractor

More information

TIm 206 Lecture notes Decision Analysis

TIm 206 Lecture notes Decision Analysis TIm 206 Lecture notes Decision Analysis Instructor: Kevin Ross 2005 Scribes: Geoff Ryder, Chris George, Lewis N 2010 Scribe: Aaron Michelony 1 Decision Analysis: A Framework for Rational Decision- Making

More information

Decision Analysis. Introduction. Job Counseling

Decision Analysis. Introduction. Job Counseling Decision Analysis Max, min, minimax, maximin, maximax, minimin All good cat names! 1 Introduction Models provide insight and understanding We make decisions Decision making is difficult because: future

More information

- Economic Climate Country Decline Stable Improve South Korea Philippines Mexico

- Economic Climate Country Decline Stable Improve South Korea Philippines Mexico 1) Micro-comp is a Toronto based manufacturer of personal computers. It is planning to build a new manufacturing and distribution facility in South Korea, Philippines, or Mexico. The profit (in $ millions)

More information

Decision Analysis under Uncertainty. Christopher Grigoriou Executive MBA/HEC Lausanne

Decision Analysis under Uncertainty. Christopher Grigoriou Executive MBA/HEC Lausanne Decision Analysis under Uncertainty Christopher Grigoriou Executive MBA/HEC Lausanne 2007-2008 2008 Introduction Examples of decision making under uncertainty in the business world; => Trade-off between

More information

DECISION ANALYSIS WITH SAMPLE INFORMATION

DECISION ANALYSIS WITH SAMPLE INFORMATION DECISION ANALYSIS WITH SAMPLE INFORMATION In the previous section, we saw how probability information about the states of nature affects the expected value calculations and therefore the decision recommendation.

More information

19 Decision Making. Expected Monetary Value Expected Opportunity Loss Return-to-Risk Ratio Decision Making with Sample Information

19 Decision Making. Expected Monetary Value Expected Opportunity Loss Return-to-Risk Ratio Decision Making with Sample Information 19 Decision Making USING STATISTICS @ The Reliable Fund 19.1 Payoff Tables and Decision Trees 19.2 Criteria for Decision Making Maximax Payoff Maximin Payoff Expected Monetary Value Expected Opportunity

More information

36106 Managerial Decision Modeling Decision Analysis in Excel

36106 Managerial Decision Modeling Decision Analysis in Excel 36106 Managerial Decision Modeling Decision Analysis in Excel Kipp Martin University of Chicago Booth School of Business October 19, 2017 Reading and Excel Files Reading: Powell and Baker: Sections 13.1,

More information

Chapter 4: Decision Analysis Suggested Solutions

Chapter 4: Decision Analysis Suggested Solutions Chapter 4: Decision Analysis Suggested Solutions Fall 2010 Que 1a. 250 25 75 b. Decision Maximum Minimum Profit Profit 250 25 75 Optimistic approach: select Conservative approach: select Regret or opportunity

More information

Decision Analysis Models

Decision Analysis Models Decision Analysis Models 1 Outline Decision Analysis Models Decision Making Under Ignorance and Risk Expected Value of Perfect Information Decision Trees Incorporating New Information Expected Value of

More information

ESD.71 Engineering Systems Analysis for Design

ESD.71 Engineering Systems Analysis for Design ESD.71 Engineering Systems Analysis for Design Assignment 4 Solution November 18, 2003 15.1 Money Bags Call Bag A the bag with $640 and Bag B the one with $280. Also, denote the probabilities: P (A) =

More information

Making Hard Decision. ENCE 627 Decision Analysis for Engineering. Identify the decision situation and understand objectives. Identify alternatives

Making Hard Decision. ENCE 627 Decision Analysis for Engineering. Identify the decision situation and understand objectives. Identify alternatives CHAPTER Duxbury Thomson Learning Making Hard Decision Third Edition RISK ATTITUDES A. J. Clark School of Engineering Department of Civil and Environmental Engineering 13 FALL 2003 By Dr. Ibrahim. Assakkaf

More information

Monash University School of Information Management and Systems IMS3001 Business Intelligence Systems Semester 1, 2004.

Monash University School of Information Management and Systems IMS3001 Business Intelligence Systems Semester 1, 2004. Exercise 7 1 : Decision Trees Monash University School of Information Management and Systems IMS3001 Business Intelligence Systems Semester 1, 2004 Tutorial Week 9 Purpose: This exercise is aimed at assisting

More information

Project Risk Analysis and Management Exercises (Part II, Chapters 6, 7)

Project Risk Analysis and Management Exercises (Part II, Chapters 6, 7) Project Risk Analysis and Management Exercises (Part II, Chapters 6, 7) Chapter II.6 Exercise 1 For the decision tree in Figure 1, assume Chance Events E and F are independent. a) Draw the appropriate

More information

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Decision Analysis

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Foundations of Decision Analysis Resource Allocation and Decision Analysis (ECON 800) Spring 04 Foundations of Decision Analysis Reading: Decision Analysis (ECON 800 Coursepak, Page 5) Definitions and Concepts: Decision Analysis a logical

More information

INTERNATIONAL UNIVERSITY OF JAPAN Public Management and Policy Analysis Program Graduate School of International Relations

INTERNATIONAL UNIVERSITY OF JAPAN Public Management and Policy Analysis Program Graduate School of International Relations Hun Myoung Park (5/2/2018) Decision Analysis: 1 INTERNATIONAL UNIVERSITY OF JAPAN Public Management and Policy Analysis Program Graduate School of International Relations DCC5350/ADC5005 (2 Credits) Public

More information

Textbook: pp Chapter 11: Project Management

Textbook: pp Chapter 11: Project Management 1 Textbook: pp. 405-444 Chapter 11: Project Management 2 Learning Objectives After completing this chapter, students will be able to: Understand how to plan, monitor, and control projects with the use

More information

Applying Risk Theory to Game Theory Tristan Barnett. Abstract

Applying Risk Theory to Game Theory Tristan Barnett. Abstract Applying Risk Theory to Game Theory Tristan Barnett Abstract The Minimax Theorem is the most recognized theorem for determining strategies in a two person zerosum game. Other common strategies exist such

More information

Answers to chapter 3 review questions

Answers to chapter 3 review questions Answers to chapter 3 review questions 3.1 Explain why the indifference curves in a probability triangle diagram are straight lines if preferences satisfy expected utility theory. The expected utility of

More information

Maximizing Winnings on Final Jeopardy!

Maximizing Winnings on Final Jeopardy! Maximizing Winnings on Final Jeopardy! Jessica Abramson, Natalie Collina, and William Gasarch August 2017 1 Introduction Consider a final round of Jeopardy! with players Alice and Betty 1. We assume that

More information

Project Risk Evaluation and Management Exercises (Part II, Chapters 4, 5, 6 and 7)

Project Risk Evaluation and Management Exercises (Part II, Chapters 4, 5, 6 and 7) Project Risk Evaluation and Management Exercises (Part II, Chapters 4, 5, 6 and 7) Chapter II.4 Exercise 1 Explain in your own words the role that data can play in the development of models of uncertainty

More information

Decision Theory. Mário S. Alvim Information Theory DCC-UFMG (2018/02)

Decision Theory. Mário S. Alvim Information Theory DCC-UFMG (2018/02) Decision Theory Mário S. Alvim (msalvim@dcc.ufmg.br) Information Theory DCC-UFMG (2018/02) Mário S. Alvim (msalvim@dcc.ufmg.br) Decision Theory DCC-UFMG (2018/02) 1 / 34 Decision Theory Decision theory

More information

1. A is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes,

1. A is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, 1. A is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. A) Decision tree B) Graphs

More information

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Fundamentals of Managerial and Strategic Decision-Making

Resource Allocation and Decision Analysis (ECON 8010) Spring 2014 Fundamentals of Managerial and Strategic Decision-Making Resource Allocation and Decision Analysis ECON 800) Spring 0 Fundamentals of Managerial and Strategic Decision-Making Reading: Relevant Costs and Revenues ECON 800 Coursepak, Page ) Definitions and Concepts:

More information

Mathematics 235 Robert Gross Homework 10 Answers 1. Joe Plutocrat has been approached by 4 hedge funds with 4 different plans to minimize his taxes.

Mathematics 235 Robert Gross Homework 10 Answers 1. Joe Plutocrat has been approached by 4 hedge funds with 4 different plans to minimize his taxes. Mathematic35 Robert Gross Homework 10 Answers 1. Joe Plutocrat has been approached by 4 hedge funds with 4 different plans to minimize his taxes. The unknown state of nature is a combination of what the

More information

ECON 312: MICROECONOMICS II Lecture 11: W/C 25 th April 2016 Uncertainty and Risk Dr Ebo Turkson

ECON 312: MICROECONOMICS II Lecture 11: W/C 25 th April 2016 Uncertainty and Risk Dr Ebo Turkson ECON 312: MICROECONOMICS II Lecture 11: W/C 25 th April 2016 Uncertainty and Risk Dr Ebo Turkson Chapter 17 Uncertainty Topics Degree of Risk. Decision Making Under Uncertainty. Avoiding Risk. Investing

More information

MGS 3100 Business Analysis. Chapter 8 Decision Analysis II. Construct tdecision i Tree. Example: Newsboy. Decision Tree

MGS 3100 Business Analysis. Chapter 8 Decision Analysis II. Construct tdecision i Tree. Example: Newsboy. Decision Tree MGS 3100 Business Analysis Chapter 8 Decision Analysis II Decision Tree An Alternative e (Graphical) Way to Represent and Solve Decision Problems Under Risk Particularly l Useful lfor Sequential Decisions

More information

Choose between the four lotteries with unknown probabilities on the branches: uncertainty

Choose between the four lotteries with unknown probabilities on the branches: uncertainty R.E.Marks 2000 Lecture 8-1 2.11 Utility Choose between the four lotteries with unknown probabilities on the branches: uncertainty A B C D $25 $150 $600 $80 $90 $98 $ 20 $0 $100$1000 $105$ 100 R.E.Marks

More information

Thursday, March 3

Thursday, March 3 5.53 Thursday, March 3 -person -sum (or constant sum) game theory -dimensional multi-dimensional Comments on first midterm: practice test will be on line coverage: every lecture prior to game theory quiz

More information

PERT 12 Quantitative Tools (1)

PERT 12 Quantitative Tools (1) PERT 12 Quantitative Tools (1) Proses keputusan dalam operasi Fundamental Decisin Making, Tabel keputusan. Konsep Linear Programming Problem Formulasi Linear Programming Problem Penyelesaian Metode Grafis

More information

Decision Analysis CHAPTER 19 LEARNING OBJECTIVES

Decision Analysis CHAPTER 19 LEARNING OBJECTIVES CHAPTER 19 Decision Analysis LEARNING OBJECTIVES This chapter describes how to use decision analysis to improve management decisions, thereby enabling you to: 1. Make decisions under certainty by constructing

More information

P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU GTBL GTBL032-Black-v13 January 22, :43

P1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU GTBL GTBL032-Black-v13 January 22, :43 CHAPTER19 Decision Analysis LEARNING OBJECTIVES This chapter describes how to use decision analysis to improve management decisions, thereby enabling you to: 1. Learn about decision making under certainty,

More information

Chapter 18: Risky Choice and Risk

Chapter 18: Risky Choice and Risk Chapter 18: Risky Choice and Risk Risky Choice Probability States of Nature Expected Utility Function Interval Measure Violations Risk Preference State Dependent Utility Risk-Aversion Coefficient Actuarially

More information

Chapter 05 Understanding Risk

Chapter 05 Understanding Risk Chapter 05 Understanding Risk Multiple Choice Questions 1. (p. 93) Which of the following would not be included in a definition of risk? a. Risk is a measure of uncertainty B. Risk can always be avoided

More information

Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017

Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017 Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.

More information

Decision Analysis CHAPTER 19

Decision Analysis CHAPTER 19 CHAPTER 19 Decision Analysis LEARNING OBJECTIVES This chapter describes how to use decision analysis to improve management decisions, thereby enabling you to: 1. Learn about decision making under certainty,

More information

EVPI = EMV(Info) - EMV(A) = = This decision tree model is saved in the Excel file Problem 12.2.xls.

EVPI = EMV(Info) - EMV(A) = = This decision tree model is saved in the Excel file Problem 12.2.xls. 1...1 EMV() = 7...6.1 1 EMV() = 6. 6 Perfect Information EMV(Info) = 8. =.1 = 1. =.6 =.1 EVPI = EMV(Info) - EMV() = 8. - 7. = 1.. This decision tree model is saved in the Excel file Problem 1..xls. 1.3.

More information

Decision Theory. Refail N. Kasimbeyli

Decision Theory. Refail N. Kasimbeyli Decision Theory Refail N. Kasimbeyli Chapter 3 3 Utility Theory 3.1 Single-attribute utility 3.2 Interpreting utility functions 3.3 Utility functions for non-monetary attributes 3.4 The axioms of utility

More information

Bidding Decision Example

Bidding Decision Example Bidding Decision Example SUPERTREE EXAMPLE In this chapter, we demonstrate Supertree using the simple bidding problem portrayed by the decision tree in Figure 5.1. The situation: Your company is bidding

More information

Comparison of Decision-making under Uncertainty Investment Strategies with the Money Market

Comparison of Decision-making under Uncertainty Investment Strategies with the Money Market IBIMA Publishing Journal of Financial Studies and Research http://www.ibimapublishing.com/journals/jfsr/jfsr.html Vol. 2011 (2011), Article ID 373376, 16 pages DOI: 10.5171/2011.373376 Comparison of Decision-making

More information

Chapter 23: Choice under Risk

Chapter 23: Choice under Risk Chapter 23: Choice under Risk 23.1: Introduction We consider in this chapter optimal behaviour in conditions of risk. By this we mean that, when the individual takes a decision, he or she does not know

More information

Energy and public Policies

Energy and public Policies Energy and public Policies Decision making under uncertainty Contents of class #1 Page 1 1. Decision Criteria a. Dominated decisions b. Maxmin Criterion c. Maximax Criterion d. Minimax Regret Criterion

More information

Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017

Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.

More information

BEEM109 Experimental Economics and Finance

BEEM109 Experimental Economics and Finance University of Exeter Recap Last class we looked at the axioms of expected utility, which defined a rational agent as proposed by von Neumann and Morgenstern. We then proceeded to look at empirical evidence

More information

Using the Maximin Principle

Using the Maximin Principle Using the Maximin Principle Under the maximin principle, it is easy to see that Rose should choose a, making her worst-case payoff 0. Colin s similar rationality as a player induces him to play (under

More information

Managerial Economics

Managerial Economics Managerial Economics Unit 9: Risk Analysis Rudolf Winter-Ebmer Johannes Kepler University Linz Winter Term 2015 Managerial Economics: Unit 9 - Risk Analysis 1 / 49 Objectives Explain how managers should

More information

Maximizing Winnings on Final Jeopardy!

Maximizing Winnings on Final Jeopardy! Maximizing Winnings on Final Jeopardy! Jessica Abramson, Natalie Collina, and William Gasarch August 2017 1 Abstract Alice and Betty are going into the final round of Jeopardy. Alice knows how much money

More information

TOPIC: PROBABILITY DISTRIBUTIONS

TOPIC: PROBABILITY DISTRIBUTIONS TOPIC: PROBABILITY DISTRIBUTIONS There are two types of random variables: A Discrete random variable can take on only specified, distinct values. A Continuous random variable can take on any value within

More information

Business Decision Making Winter semester 2013/2014 (20115) February 4, Group A

Business Decision Making Winter semester 2013/2014 (20115) February 4, Group A Business Decision Making Winter semester 2013/2014 (20115) February 4, 2014 Name:............................................. Student identification number:................... Group A This eam consists

More information

Obtaining a fair arbitration outcome

Obtaining a fair arbitration outcome Law, Probability and Risk Advance Access published March 16, 2011 Law, Probability and Risk Page 1 of 9 doi:10.1093/lpr/mgr003 Obtaining a fair arbitration outcome TRISTAN BARNETT School of Mathematics

More information

Learning Objectives 6/2/18. Some keys from yesterday

Learning Objectives 6/2/18. Some keys from yesterday Valuation and pricing (November 5, 2013) Lecture 12 Decisions Risk & Uncertainty Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.centime.biz Some keys from yesterday Learning Objectives v Explain

More information

The Islamic University of Gaza Faculty of Commerce Quantitative Analysis - Prof. Dr. Samir Safi Midterm #1-15/3/2015. Name

The Islamic University of Gaza Faculty of Commerce Quantitative Analysis - Prof. Dr. Samir Safi Midterm #1-15/3/2015. Name The Islamic University of Gaza Faculty of Commerce Quantitative Analysis - Prof. Dr. Samir Safi Midterm #1-15/3/2015 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

More information

Lecture 12: Introduction to reasoning under uncertainty. Actions and Consequences

Lecture 12: Introduction to reasoning under uncertainty. Actions and Consequences Lecture 12: Introduction to reasoning under uncertainty Preferences Utility functions Maximizing expected utility Value of information Bandit problems and the exploration-exploitation trade-off COMP-424,

More information

Decision Trees: Booths

Decision Trees: Booths DECISION ANALYSIS Decision Trees: Booths Terri Donovan recorded: January, 2010 Hi. Tony has given you a challenge of setting up a spreadsheet, so you can really understand whether it s wiser to play in

More information

Handling Uncertainty. Ender Ozcan given by Peter Blanchfield

Handling Uncertainty. Ender Ozcan given by Peter Blanchfield Handling Uncertainty Ender Ozcan given by Peter Blanchfield Objectives Be able to construct a payoff table to represent a decision problem. Be able to apply the maximin and maximax criteria to the table.

More information

UNIT 10 DECISION MAKING PROCESS

UNIT 10 DECISION MAKING PROCESS UIT 0 DECISIO MKIG PROCESS Structure 0. Introduction Objectives 0. Decision Making Under Risk Expected Monetary Value (EMV) Criterion Expected Opportunity Loss (EOL) Criterion Expected Profit with Perfect

More information

Decision Making Under Risk Probability Historical Data (relative frequency) (e.g Insurance) Cause and Effect Models (e.g.

Decision Making Under Risk Probability Historical Data (relative frequency) (e.g Insurance) Cause and Effect Models (e.g. Decision Making Under Risk Probability Historical Data (relative frequency) (e.g Insurance) Cause and Effect Models (e.g. casinos, weather forecasting) Subjective Probability Often, the decision maker

More information

DECISION THEORY AND THE NORMAL DISTRIBUTION M ODULE 3 LEARNING OBJECTIVE MODULE OUTLINE

DECISION THEORY AND THE NORMAL DISTRIBUTION M ODULE 3 LEARNING OBJECTIVE MODULE OUTLINE M ODULE 3 DECISION THEORY AND THE NORMAL DISTRIBUTION LEARNING OBJECTIVE After completing this module, students will be able to: 1. Understand how the normal curve can be used in performing break-even

More information