Decision Technology Modeling, Software and Applications Matthew J. Liberatore Robert L. Nydick John Wiley & Sons, Inc. Chapter 9 Introduction to Decision Making INTRODUCTION Classical decision analysis and the Analytic Hierarchy Process (AHP) provide structure and guidance for thinking systematically about making complex decisions. Examples include: Which job offer should I accept? Where should my company locate a new service facility? Should my local government offer a tax amnesty program to increase revenues? INTRODUCTION Decisions such as these are characterized by uncertainty, conflicting multiple objectives, and differing perspectives of the various affected stakeholders. The recommendations offered by decision analysis should not be blindly accepted. The process and its results should be viewed as an important source of information for making decisions. INTRODUCTION We distinguish between a good decision and a good outcome. Decision analysis improves your chances for a good outcome and reduces your chances for an unpleasant outcome. INTRODUCTION Why might decision analysis not produce a good outcome? There are a lot of reasons! - you bought a car and got a lemon. - when buying a car fuel economy was not important to you, however, you were recently transferred and now you have a 50 minute commute. CLASSICAL DECISION ANALYSIS Suppose you inherited the following lottery. CLASSICAL DECISION ANALYSIS Suppose you inherited the following lottery. 0.50 $1000 L1 0.50 $0 CLASSICAL DECISION ANALYSIS Suppose you inherited the following lottery. 0.50 $1000 L1 0.50 $0 What amount makes you indifferent between selling the lottery or keeping the lottery and playing? CLASSICAL DECISION ANALYSIS Suppose you inherited the following lottery. 0.50 $1000 L1 0.50 $0 Amount 1000 999 998 ... 2 1 0 Decision Sell Sell Sell ... Keep Keep Keep What amount makes you indifferent between selling the lottery or keeping the lottery and playing? EXPECTED MONETARY VALUE The expected monetary value (EMV) is a long run average and is computed as: EMV = (Pi)(Xi) EMV = Expected monetary value Pi = probability of event i Xi = payoff of event i EXPECTED MONETARY VALUE For the above lottery: EMV = (0.50)(1000) + (0.50)(0) = $500 Most would sell for less than $500. EMV does not consider risk. Many factors influence your attitude including wealth and personal beliefs. EXPECTED MONETARY VALUE Example 1 (Lawsuit settlement): Choose one of the following: A1: $100,000 gift, tax free, for sure; A2: Flip a fair coin; if heads then receive $0, if tails then receive a $250,000 tax free gift. Example 2 (Insurance): Choose one of the following: B1: $1000 loss; B2: 0.0006 chance of a $1,000,000 loss and 0.9994 chance of no loss. EXPECTED MONETARY VALUE Example 3 (A paradox): Choose one of the following: C1: $10,000 gift tax free, for sure; C2: 2N cents, where N is the number of coin flips until the first tails occurs. Which alternatives do you prefer? Most people would choose A1, B1, and C1. However, EMV decision makers would prefer A2, B2, and C2 (EMV(A2)=125000, EMV(B2)=-$600, and EMV(C2)=?). Example 3 is known as the St. Petersburg Paradox. EXPECTED MONETARY VALUE The EMV of the St. Petersburg Paradox. N p(N) 2N Result 1 (1/2)1 21 T 2 (1/2)2 22 HT 3 (1/2)3 23 HHT 4 (1/2)4 24 HHHT ... EXPECTED MONETARY VALUE The EMV of the St. Petersburg Paradox. N p(N) 2N Result 1 (1/2)1 21 T 2 (1/2)2 22 HT 3 (1/2)3 23 HHT 4 (1/2)4 24 HHHT ... EMV= (1/2)1*21 + (1/2)2*22 + (1/2)3*23 + (1/2)4*24 + ... = 1 + 1 + 1 + + ... = infinity! 1 UTILITY THEORY EMV is a long run average and does not consider risk. Von Neumann and Morgenstern argued that people maximize expected utility. This assumes that a utility function can be determined for each individual or group for a given problem situation. UTILITY THEORY The utility function expresses an attitude toward risk. In a given situation, some people may be risk neutral, risk averse, or risk loving. Recall, the first lottery of a 50/50 chance of winning $0 or $1000. Those that value the lottery at $500 are risk neutral EMVers. Those that value the lottery at less than $500 are risk averse, while those that value the lottery at more than $500 are risk loving. UTILITY THEORY A utility function for a risk averse person is upward sloping and concave. U(X) 0 X ESTIMATING UTILITY FUNCTIONS Utility functions can be estimated by developing a series of indifference points between receiving a certain amount and taking a gamble or lottery. Reconsider the first lottery of a 50/50 chance of winning $0 or $1000. 1. Set anchor utility values: U(1000)=1 and U(0)=0. 2. Suppose you are indifferent between receiving $300 or keeping the lottery. This implies that: U(300)=EU(lottery) = .5*U(1000) + .5*U(0) = 0.5 ESTIMATING UTILITY FUNCTIONS 3. Other points on the utility curve can be defined by finding indifference values for other lotteries. a.Consider the lottery of a 50/50 chance of winning $1000 or $300. Suppose you are indifferent for $400. Then, U(400)=EU(lottery)=.5*U(1000) + .5*U(300) = 0.75 b.Consider the lottery of a 50/50 chance of winning $300 or $0. Suppose you are indifferent for $50. Then, U(50)=EU(lottery)=.5*U(300) + .5*U(0) = 0.25 ESTIMATING UTILITY FUNCTIONS Using these five points, a utility curve can be drawn. U(X) Piecewise concave 1 utility curve 0.75 EMV 0.50 0.25 0 50 300 400 1000 X PROBLEMS WITH UTILITY There are several problems with utility theory that must be addressed in practice. 1. It is assumed that the decision maker is perfectly consistent in their beliefs about utility. From the utility curve that we just estimated, we know that U(50)=0.25, U(300)=0.50, and U(400)=0.75. This implies that, U(300)=2*U(50), U(400)=1.5*U(300), so U(400)=3*U(50). PROBLEMS WITH UTILITY This might be acceptable in some cases, but suppose we have estimated a utility curve for market share. We find that: U(30%)=2*U(20%) and U(20%)=1.5*U(15%). Utility theory requires us to believe that U(30%)=3*U(15%). PROBLEMS WITH UTILITY In fact, when considering this comparison, we might find that U(30%) might be 4 or 5 times U(15%). Individuals are not always perfectly consistent in their judgments and this does not mean that they are illogical! PROBLEMS WITH UTILITY 2. The use of lotteries to determine a utility curve is artificial since individuals are asked to make hypothetical choices and use this information to solve real problems. 3. Utility functions must be anchored on a fixed scale. What happens when phenomena must be evaluated that are outside the range of the scale? PROBLEMS WITH UTILITY 4. Utility curves can only be developed if numbers can be assigned to the relevant criteria. How do you develop a utility curve to measure intangible and highly subjective factors, such as style, when deciding what car to purchase? PROBLEMS WITH UTILITY For these and other reasons, managers often make decisions that are inconsistent with the maximization of expected utility. That is, expected utility often is not descriptive of actual decision making behavior, even though it is appealing from a prescriptive point of view. Would you use expected utility to help make a major business decision? A major personal decision? THE AHP The Analytic Hierarchy Process (AHP) is an alternate approach to expected utility. AHP successfully addresses the limitations of expected utility. AHP is implemented using the software package called Decision Lens. THE AHP What is the Analytic Hierarchy Process (AHP)? The AHP, developed by Tom Saaty, is a decision-making method for prioritizing alternatives when multi-criteria must be considered. An approach for structuring a problem as a hierarchy or set of integrated levels. THE AHP AHP problems are structured in at least three levels: The goal, such as selecting the best car to purchase, The criteria, such as cost, safety, and appearance, The alternatives, namely the cars themselves. THE AHP The decision-maker: measures the extent to which each alternative achieves each criterion, and determines the relative importance of the criteria in meeting the goal, and synthesizes the results to determine the relative importance of the alternatives in meeting the goal. THE AHP How does AHP capture human judgments? AHP never requires you to make an absolute judgment or assessment. You would never be asked to directly estimate the weight of a stone in kilograms. AHP does require you to make a relative assessment between two items at a time. AHP uses a ratio scale of measurement. APPROACH Suppose the weights of two stones are being assessed. AHP would ask: How much heavier (or lighter) is stone A compared to stone B? AHP might tell us that, of the total weight of stones A and B, stone A has 65% of the total weight, whereas, stone B has 35% of the total weight. APPROACH Individual AHP judgments are called pairwise comparisons. These judgments can be based on objective or subjective information. For example, smoothness might be a subjective criterion used to compare two stones. Pairwise comparisons could be based on touch. APPROACH However, suppose stone A is a diamond worth $1,000.00 and stone B is a ruby worth $300.00. This objective information could be used as a basis for a pairwise comparison based on the value of the stones. APPROACH Consistency of judgments can also be measured. Consistency is important when three or more items are being compared. Suppose we judge a basketball to be twice as large as a soccer ball and a soccer ball to be three times as large as a softball. To be perfectly consistent, a basketball must be six times as large as a softball. APPROACH AHP does not require perfect consistency, however, it does provide a measure of consistency. We will discuss consistency in more detail later. AHP APPLICATIONS AHP has been successfully applied to a variety of problems. 1. R&D projects and research papers; 2. vendors, transport carriers, and site locations; 3. employee appraisal and salary increases; 4. product formulation and pharmaceutical licensing; 5. capital budgeting and strategic planning; 6. surgical residents, medical treatment, and diagnostic testing. AHP APPLICATIONS The product and service evaluations prepared by consumer testing services is another potential application. Products and services, such as self propelled lawn mowers are evaluated. Factors include: bagging, mulching, discharging, handling, and ease of use. An overall score for each mower is determined. AHP APPLICATIONS Would you make your purchasing decision based solely on this score? Probably not! Some of the information will be helpful. Some additional questions are: How important is each criterion? Would you weigh the criteria the same way? Are all of the criteria considered important to you? Are there other criteria that are important to you? Have you ever thought about these issues? RANKING SPORTS RECORDS The AHP has been used to rank outstanding season, career, and single event records across sports. Season 1. Babe Ruth, 1920: .847 slugging average 2. Joe DiMaggio, 1944: 56 game hitting streak 3. Wilt Chamberlain, 1961-62: 50.4 points per game scoring average RANKING SPORTS RECORDS Career 1. Johnny Unitas, 1956-70: touchdown passes in 47 consecutive games 2. Babe Ruth, 1914-35: .690 slugging average 3. Walter Payton, 1975-86: 16,193 rushing yardage Single event 1. Wilt Chamberlain, 1962: 100 points scored 2. Norm Van Brocklin, 1951: 554 passing yards 3. Bob Beamon, 1968: 29' 2.5" long jump RANKING SPORTS RECORDS How do we compare records from different sports? It all depends on the criteria that you select! Golden and Wasil (1987) used the following criteria: 1. Duration of record - years record has stood, years expected to stand 2. Incremental improvement - % better than previous record 3. Other record characteristics - glamour, purity (single person vs. team) RANKING SPORTS RECORDS Did this article end all arguments about sports records? Absolutely not! In bars and living rooms across the country, people still argue about sports. AHP provides a methodology to structure the debate. Different criteria and different judgments could produce different results. A FINAL POINT ABOUT SPORTS In reading the sports pages we often see discussion of how well teams match up across different positions. These match-ups are often used to predict a winner. Match-ups are a pairwise comparison concept! AHP APPLICATIONS Our culture is obsessed with quantitative rankings of all sorts of things. There are many measurement problems associated with rankings of products, sports teams, universities, and the like. Many of these issues are discussed on a web site at: http://www.expertchoice.com/annie.person APPLES AND ORANGES The discussion of how to compare records from different sports recalls a saying from childhood: APPLES AND ORANGES The discussion of how to compare records from different sports recalls a saying from childhood: You can’t compare apples and oranges. All you get is mixed fruit! APPLES AND ORANGES The discussion of how to compare records from different sports recalls a saying from childhood: You can’t compare apples and oranges. All you get is mixed fruit! After the discussion about sports, do you still believe this statement? APPLES AND ORANGES The discussion of how to compare records from different sports recalls a saying from childhood: You can’t compare apples and oranges. All you get is mixed fruit! After the discussion about sports, do you still believe this statement? We hope not!!! APPLES AND ORANGES What criteria might you use when comparing apples and oranges? There are a vast set of criteria that may change depending upon time of day or season of year: taste, ripeness, shape, cost. texture, juiciness, weight, Can you think of others? smell, nutrition, color, and APPLES AND ORANGES The point is that people are often confronted with the choice between apples and oranges. Their choice is based on some psychological assessment of: relevant criteria, their importance, and how well the alternatives achieve the criteria. Slippery Rock Number 1 In 1936 there was no consensus about the number 1 college football team. Some experts argued that the University of Minnesota should be number 1 while others argued that it should be the University of Pittsburgh. One expert thought that Slippery Rock, a small college in western Pennsylvania, should be number 1. His reasoning is: – – – – – Slippery Rock defeated West Virginia West Virginia defeated Duquesne Duquesne defeated Pitt Pitt defeated Notre Dame Notre Dame defeated Minnesota Do you believe this argument? Number 1 Restaurant in Philadelphia In 1999 Zagat’s survey rated the Fountain as the number 1 restaurant in Philadelphia with perennial winner Le BecFin dropping to the number 2 spot. How did this happen? – Zagat relies on ordinary diners to rate restaurants – Nearly 1000 people voted for Philadelphia restaurants – People rated each of three categories (Food, Décor, and Service) on a 0-3 scale, where 3 is perfection – Zagat averages the numbers (An average of 2.6 translates to a 26) – The numbers are then rounded Number 1 Restaurant in Philadelphia The results: Food Décor Service Total Le Bec-Fin 29.14 (29) 28.36 (28) 28.67 (29) 86.17 (86) Fountain 28.88 (29) 28.68 (29) 28.59 (29) 86.15 (87) Zagat rated the Fountain number 1 because their rounded score beat Le Bec-Fin’s rounded score. What do you think? SUMMARY This chapter provided an introduction to decision making. Specific topics covered include: Expected Monetary Value, Utility Theory, and an introduction to the Analytic Hierarchy Process. COPYRIGHT Copyright 2003Matthew J. Liberatore and Robert L. Nydick. All rights reserved. Reproduction or translation of this work beyond that named in Section 117 of the United States Copyright Act without the express written consent of the copyright owners is unlawful. Requests for further information should be addressed to Matthew J. Liberatore and Robert L. Nydick. Adopters of the textbook are granted permission to make back-up copies for their own use only, to make copies for distribution to students of the course the textbook is used in, and to modify this material to best suit their instructional needs. Under no circumstances can copies be made for resale. Matthew J. Liberatore and Robert L. Nydick assume no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.