1. ISE 195 Introduction to Industrial Engineering

2. Lecture 4 Decision Analysis

3. 3 Decision Analysis What is the hardest decision you have ever had to make? Since we all have to make decisions, we are all Decision Makers of a sort and can benefit from the study of decision making. Have you ever had to make a decision and then later have to explain or defend that decision?

4. 4 Decision Domains Personal domain  Where to live; college to attend; car to buy; etc Business domain  Introduce the new product; bid on a contract; hire Government domain  How to allocate money; where to get involved

5. 5 Decision Roles Those who study decisions will be referred to as decision analysts while those that make the decisions will be referred to as the decision makers. Why do you think we would want to separate the roles of the decision analyst and the decision maker? Proper decision making requires collaboration among the decision makers and the decision analysts in order to find the best solution based on insights versus position

6. 6 Why Decisions Are Hard Decisions are hard for a number of structural, emotional, and organizational reasons  Structural – uncertainty, trade-offs, complexity  Emotional – anxiety, multiple objectives, competition  Organizational – lack of consensus, differing perspectives

7. 7 Why Decisions Are Hard Do you think your personal decisions are going to be easier or harder than the decisions you might be faced with in business (engineering)? What might be some of the reasons, both obvious and less obvious, for this difference in level of complexity between decisions from the personal domain and decisions from the business or government domain?

8. 8 Why Decisions Are Hard There are other reasons decisions are hard  Consequences  Uncertainty  Ambiguity

9. 9 Why Decisions Are Hard Ambiguity Consequences Uncertainty CAU Model, Skinner HIGH MEDIUM LOW

10. 10 Why Decisions Are Hard Ambiguity Consequences Uncertainty CAU Model, Skinner

11. 11 What Makes A Good Decision What is a good decision? What is a good outcome? Does a good decision always lead to a good outcome?  Name some examples... A good decision emerges as the result of valid decision making process (of which there are a few as we will see)

12. 12 “When you come to a fork in the road, take it” - Yogi Berra

13. 13 History Operational research, quantitative management, based on repetitive actions  Focused on optimizing objectives and meeting constraints Failed to focus on needs of executive decision making  In particular their more complex, strategic problems Technique needed for logical guidance on complex, uncertain situations DA combines systems analysis and statistical decision theory

14. 14 History Problems typical of DA application are:  Unique  Important  Contain uncertainty  Have long-run implications  Contain complex preferences DA arose in the late 60s, early 70s and balances the following OR considerations:  Mathematical modeling  Computer implementation  Quantitative analysis and decision making

15. 15 History DA also incorporated the following aspects of human decision making  Management experience  Management judgment  Management preferences The art of DA involves “capturing” the above from the managers and decision makers  The techniques used to capture the above are sometimes controversial within the operational research / systems engineering field

16. 16 Terminology Decision  A conscious irrevocable allocation of resources with the purpose of achieving a desired objective Uncertainty  Something that is unknown or not perfectly known Outcomes  Depend on alternative chosen and the uncertainties impacting it Value  Something the decision maker wants and can tradeoff

17. 17 Terminology Objective  Something specific the decision maker wants to achieve Decision Maker  Anyone with the authority to allocate the necessary resources for the decision being made Subjective Probability  Classical approach to probability called the “frequentist” approach  Subjective approach, the Bayesian, allows that each of us can provide valid probabilities

18. 18 Probabilistic Methods (Pay attention is ISE 301!) These assume the possible outcomes (states of nature) can be assigned probabilities that represent their likelihood of occurrence.These assume the possible outcomes (states of nature) can be assigned probabilities that represent their likelihood of occurrence. ­Also referred to as methods for decision making under “risk”

19. 19 Expected Monetary Value u Selects alternative with the largest expected monetary value (EMV)  EMV i is the average payoff we would receive if we faced the same decision problem numerous times and always selected alternative i.

20. 20 Decision Trees Graphical means for displaying a decision problem that shows, in chronological order:  the alternatives available to the decision maker;  the futures that could be experienced; and  the consequences of choosing between alternatives Trees consist of:  Branches — lines representing possible “decision paths”  Decision Forks — “nodes” which represent choices to be made by the decision maker; and  Chance Forks — nodes which represent possible futures that are modeled as selected by nature

21. 21 Decision Trees (continued) To “evaluate” a tree one must:  assign values of an appropriate evaluation measure to each branch (often summarized at the end of the branch); and  choose branches appropriately at each decision node, working from right to left  When making decisions under risk, this entails: –assigning probabilities to each branch emanating from a chance fork; –computing expected values at each chance node; and –finding the branch that maximizes the expected value from among all branches emanating from a decision fork.

22. 22 Example – Electronics Firm An electronics firm makes components that are sold and shipped to an automobile manufacturer.  Five percent of all components produced are defective due to poor solder connections.  Can’t tell if defective until after it is installed on a car. –Auto maker will charge the electronics firm $800 per defective component to cover the cost of repair. A proposal: double-solder each component before before it is shipped to the automobile maker.  Will cost $50 per component to double-solder but is sure to eliminate this cause of defective components –i.e., no double-soldered components will be defective.

23. 23 Is the proposal worthwhile?  Assume electronics firm seeks to minimize its expected cost and consider using our structure:  Actions:1 -- double solder before shipping 2 -- do not double solder  Outcomes:1 -- component is defective 2 -- component is good  Prior Probabilities:P 1 = 0.05; P 2 = 0.95 –Note that these probabilities apply only if the component is not double-soldered!  Value Function:E 11 = -50; E 12 = -50; E 21 = -800; E 22 = 0 Example – Electronics Firm ( Continued) “Values” are “negative” costs here

24. 24 Electronics Firm – Decision Tree  Expected Values: -- Double-Solder:E(V) 1 = -50 Do Not:E(V) 2 = -800(0.05) + 0(0.95) = -40 »No, it would not be worthwhile to double-solder every component since the maximum expected value (minimum expected cost) is obtained for action 2 (do not double-solder).  Decision Tree: Do Not Double Solder Good (0.95) Defective (0.05) -50 -800 0 -40 X

25. 25 To this point, we have assumed that the firm is unable to tell if a component is defective until after it is installed on a car.  Obviously, if the firm were to know in advance that a component was defective, it would double-solder that component.  A reasonable strategy, then, might be to attempt to determine whether or not a component is defective before the decision to double-solder or not is made.  How much should the firm be willing to pay to for this sort of information? Example – Doing Better?

26. 26 Example – Paying for More Information  Without any advance info about components, the firm’s best strategy is to not double-solder any components –This has an expected cost of $40 per component.  With advance info, however, the firm should:  double-solder all defective components at a cost of $50 each, and  not double-solder the rest (the good components).  Since 5% of all components are defective, the expected cost of this strategy would be: –$50(0.05) + 0(0.95) = $2.50 per component.  Thus, the most the firm should be willing to pay for this advance info is the difference between these, or $40 - 2.50 = $37.50 per component.

27. 27 Getting Advance Information “Advance information” can often be obtained by performing some sort of test before making a decision  If so, then the initial choice we must make is whether or not to do the testing The ideal situation would be one in which the testing enables us to correctly predict the future  In our example, this would mean that the test is 100% accurate in classifying components as good or defective –e.g., if the test classifies a component as “defective,” then that component is indeed defective.

28. 28 Decision Tree w/ Perfect Testing We assume here that “testing” is “perfect,” so that all components will be correctly classified and, thus, 95% will be classified as “good” while 5% will be classified as “defective” No Action Double Solder Good (0.95) Defective (0.05) Do Not Test Perform Test (Get Advance Info) Classify as Defective (0.05) Classify as Good (0.95) -50 -800 0 No Action Double Solder Good (0.00) Defective (1.00) -50 -800 0 No Action Good (1.00) Defective (0.00) -50 -800 0 0 0 X -50 X -40 X -2.5 Double Solder

29. 29 Bayesian Decision Making A method for accounting for the effects of advance testing in decision making Based on Bayes’ Theorem which provides us a way to “revise” our initial “prior” probabilities for the occurrence of each possible future given the results of testing

30. 30 Example – Revisited Suppose now that the firm can choose to test each component, at a cost of $20 apiece, to see if the component might be defective before the decision to double-solder or not is made.  The test is not perfect, but they have a track record  Based on the results of testing known good and known defective components, it is determined that: –the test will incorrectly classify 15% of all defective components as good, and –incorrectly classify 10% of all good components as defective.  Is it worthwhile for the firm to perform this test?

31. 31 Decision Tree w/ Testing To evaluate this tree and decide what to do, we need to fill in appropriate probabilities at all chance forks. No Action Double Solder Good (0.95) Defective (0.05) Do Not Test Perform Test Classify as Defective (???) Classify as Good (???) -50 -800 0 No Action Double Solder Good (???) Defective (???) -50 -800 0 No Action Double Solder Good (???) Defective (???) -50 -800 0 -40 X -20

32. 32 Example – Description of Test  Note that there are two possible results when a component is subjected to the proposed test: Result 1: The component is classified as defective Result 2: The component is classified as good  The particular result to be obtained will depend on both:  the state of nature (the condition of the component being tested), and,  since the experiment is not perfect, also on chance.  What we know about the accuracy of the test is captured by the conditional probabilities of obtaining a particular result given a particular state of nature...

33. 33  That is, we “know” that our experiment will incorrectly classify 15% of all defective components as good and 10% of all good components as defective.  We denote this using the notation: »P[component classified as defective | it is defective] = P[Result 1 | State of nature 1]  Q 1|1 = 0.85 »P[component classified as good | it is defective] = P[Result 2 | State of nature 1]  Q 2|1 = 0.15 »P[component classified as defective | it is good] = P[Result 1 | State of nature 2]  Q 1|2 = 0.10 »P[component classified as good | it is good] = P[Result 2 | State of nature 2]  Q 2|2 = 0.90 –Unfortunately, these are not the probabilities we need to complete the decision tree! Description of Test – Continued

34. 34 Bayes’ Theorem To compute the conditional probabilities of encountering each possible future given the results of the test, we combine previous results to obtain:  Bayes’ Theorem: If are n mutually exclusive and exhaustive events defined over a sample space and E is any other event with P[E] > 0, then  Bottom Line: the posterior probability of encountering state of nature j (j = 1, 2,..., m) given that the test produces result k (k = 1, 2,..., r) can be found via: Bayes’ Rule The Law of “Total Probability”

35. 35 Example – Posterior Probabilities  For the electronics firm, we can then compute: P 1|1 = P[component is defective | classified as defective] = P[State of nature 1|Result 1] = P[Result 1|State of nature 1]  P[State of nature 1]  P[Result 1] = Q 1|1 P 1 /Q 1 = (0.85)(0.05)/(0.1375)  0.3091  Likewise P 2|1 = P[component is good |classified as defective] = P[State of nature 2|Result 1] = Q 1|2 P 2 /Q 1 = (0.10)(0.95)/(0.1375)  0.6909

36. 36 Example – Posterior Probabilities ( Continued)  Similarly P 1|2 = P[component is defective |classified as good] = Q 2|1 P 1 /Q 2 = (0.15)(0.05)/(0.8675)  0.0087 and P 2|2 = P[component is good |classified as good] = Q 2|2 P 2 /Q 2 = (0.90)(0.95)/(0.8675)  0.9913  Terminology: the quantity Q k|j P j formed in the preceding computations is often called the joint probability of encountering state of nature j and obtaining result k from the experiment (since it is the probability of both the two events occurring).

37. 37 Example – Decision Tree (Revisited) No Action Double Solder Good (0.95) Defective (0.05) Do Not Test Perform Test Classify as Defective (0.1375) Classify as Good (0.8625) -50 -800 0 No Action Double Solder Good (0.6909) Defective (0.3091) -50 -800 0 No Action Double Solder Good (0.9913) Defective (0.0087) -50 -800 0 -40 X -20 -247.47 -50 X -6.96 X -12.88 X -32.88

38. 38 Discrete Probability Assessment Three methods for assessing discrete probability  Direct question  Assumes familiarity with probability  Usually means decision maker used to providing probabilities; based on similar experiences  Betting method  Most people bet in some fashion  “odds” provide perception of likelihood of the outcome  Use the odds to derive the probability  Reference lottery  Find probability yielding indifference point

39. 39 Experts and Assessments Reliance on experts important in complex problems Important to avoid bias in assessment and collection Protocol for expert assessment  Background  Identify and recruit experts  Motivate the experts  Structure and decompose the problem  Probability assessment training  Probability elicitation and verification  Aggregation of distributions

40. 40 Theoretical Probability Models Subjective probabilities may be difficult to get Alternative is to use some theoretical distribution  Actually making a subjective assessment via your choice A variety of distributions apply in a variety of applications  Binomial  Normal  Exponential  Triangular

41. 41 Other Decision Factors: Risk Have not worried about “risk”  Decision makers may actually have differing attitudes toward risk  Would like a model to map outcomes into measures that incorporate attitudes towards risk  In decision analysis this is accomplished using utility functions The corresponding outcomes, not measured in utilities, may provide different alternative selections than those not using utilities  Changes due to incorporation of risk

42. 42 Other Decision Factors: Multi-attribute Decisions Have focused on a single attribute Most decisions are multi-attribute in nature  Trade-off between weight and redundancy  Trade-off between reliability and maintenance Some multi-attribute models assume independence  Assess each attribute  Develop a weighting scheme for each attribute  Use weighted sum of scores  Called an “additive model”

43. 43 Multiple Attributes Reality in most multi-attribute models requires some form of interaction  Attributes are not independent  Need to derive a utility surface  Techniques for determining the surface are extensions of independent techniques  Complications come during elicitation as the expert is asked to specifically consider dependencies

44. ISE 195: Overview of Decision Analysis Questions?