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Foundations for DSS: Rationality, Utility Theory & Decision Analysis

Topics in DSS End user computing DSS concepts EIS, GDSS, groupware Rationality Frameworks for decision making Decision trees Multiattribute decision modeling Spreadsheet implementations Reading assignments (2 sessions) Zwass, DSS chapter

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Foundations for DSS: Rationality, Utility Theory & Decision Analysis

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  1. Topics in DSS End user computing DSS concepts EIS, GDSS, groupware Rationality Frameworks for decision making Decision trees Multiattribute decision modeling Spreadsheet implementations Reading assignments (2 sessions) Zwass, DSS chapter Kimbrough, MIS Notes, Part II, DSS; chapter 5, “A Brief Introduction to Decision Analysis” (skip sections 5.3-4); chapter 6, “Case: DSS Evaluation with MAUT” Kimbrough et al., AMV DSS paper Dawes, “Robust Beauty of Improper Linear Models” Foundations for DSS:Rationality, Utility Theory &Decision Analysis

  2. Concept History Motivations Packages Management issues How much? Who? + or -? etc. Examples? End User Computing

  3. S(imple) or F(ancy)? S F 90%, -$3 50%, -$1 S 10%, -$1 50%, -$1 10%, -$1 50%, -$3 F 90%, -$3 50%, -$3

  4. Data, models,…, and documents Interactively History Motivations Packages and tools Roll your own DSS generators Spreadsheets+ Management issues How much? Who? + or -? etc. Examples? DSS Concepts

  5. Data-oriented DSS Questions? Examples? Model-oriented DSS Examples? DSS application theory what if: exploration, training, insight objectivity: models, data in “public” argumentation and persuasion Development of DSS How do executives use DSS? EIS? GDSS Groupware DSS Concepts (con’t.)

  6. See, e.g., Interfaces From one recent issue: Examples of Model-BasedDSS “IMPReSS: An Automated Production-Planning and Delivery-Quotation System at Harris Corporation--Semiconductor Sector” IMPReSS has raised on-time deliveries from 75 to 95 percent without increasing inventories, enabled the sector to expand market share, and helped it to move from an annual loss of $75 million ot an annual profit of over $40 million. “Integrated Planning for Poultry Production at Sadia” Sadia has saved over $50 billion over three years using mathematical models to obtain better conversaion of feed to live bird weight, improved utilitization of birds, improved fulfillment of production plans, reduced lead times, and wide ranging studies of price and demand scenarios. “KeyCorp Service Excellence Management System” KeyCorp’s SEMS models have helpd it reduce customer processing time by 53 percent, improve customer wai time, and reduce personnel expenses. And more!

  7. "To do something rationally is to do it for good and cognet reasons. And this is not the same as just having a motive for doing it. All of us almost always act for motives, but valid reasons are...what motivate the rational agent, and most of us do not act rationally all of the time." "From the rational point of view, our mere wants have little significance. They can and should be outweighed by our interests and our needs." "Rationality is not just a matter of having some reasons for what one does, but of aligning one's beliefs, actions, and evaluations effectively with the best or strongest available reasons." Reminders on Rationality

  8. "Rationality does not make demands beyond the limits of what is genuinely possible for us---it does not require accomplishments beyond the limits of the possible. For rationality, no more is demanded of us than doing our realistic best to work efficiently and effectively towards the realization of our cognitive, practical, and evaluative goals." "To be sure, rationality is not just a passible matter of making good use of the materials one has on hand---in cognitive matters, say, the evidence in view. It is also a matter of actively seeking to enhance these materials: in the cognitive case, by developing new evidential resources that enable one to amplify and to test one's conclusions. The endeavour to make the most of one's opportunities is an aspect of intelligence that is crucial to rationality." Rationality

  9. "Rationality makes demands upon us. It speaks in didactic tones: this or that is what you should do." "Accordingly, rationality in all its forms calls for the comparative assessment of feasible alternatives, and so demands five faculties: "1. Imagination... "2. Information-processing... "3. Evaluation... "4. Selection---Informed Choice... "5. Agency: the capacity to implement choices." "Rational choice in a given situation generally requires a consideration of the wider context." All this from Rescher, Rationality. (Aunte Martha) Rationality

  10. General elements for decision making Actions--a Up to us Outcomes--o Given to us Not considering game theory here. How might we do this? Probabilities--P(o|a) Desirabilities--D(o|a) Frameworks for DecisionMaking

  11. Actions: bring red, bring white, bring rosé Outcomes, primary: Beef served Chicken served Fish Vegetarian Outcomes, net: Beef served with your red wine Beef served with your white wine ... etc. Example: Which Wine to Bring?

  12. Model with tables: (a) probabillities, (b) desirabilities, (c) net results Example: Which Wine to Bring?(con't.) Outcomes: o(j) Beef Chicken Fish Vegetarian Actions: a(i) P(o(1)|a(1)) ......................... : : : : : : : Red White Rosé P(o(j)|a(i))

  13. Example: Which Wine to Bring?(con't.) • Model with tables: (b) desirabilities Outcomes: o(j) Beef Chicken Fish Vegetarian Actions: a(i) D(o(1)|a(1)) ......................... : : : : : : : Red White Rosé D(o(j)|a(i))

  14. A reasonable rule: Pick (do) an a(1), such that D(a(i))  D(a(j)), for i ° j Example: Which Wine to Bring?(con't.) • Model with tables: (c) net results Outcomes: o(j) actions outcomes Beef Chicken Fish Vegetarian Actions: a(i) D(a(1)) D(a(2)) D(a(3)) P(o(1)|a(1))*D(o(1)|a(1)) +.... : : : : : : : Red White Rosé P(o(j)|a(i))*D(o(j)|a(i)) j

  15. Recall: general elements for decision making Actions--up to us Outcomes--given to us Probabilities--P(o|a) Desirabilities--D(o|a) But, how well do we know them? Certainty Risk (only up to a probability) Ambiguity (have only a rough idea of what the probabilities are) Uncertainty (have no idea what the probabilities are) Frameworks for DecisionMaking

  16. In addition, we may or may not have a complete list of the Actions Outcomes Decision making can become complex How many cells in this framework? Two levels of completeness and four levels of knowledge (but not applying to actions, assume we have them with certainty), then the combinations are: a: 2, o: 4*2, p: 4*2, d: 4*2, or • 2*3^8 = 13,122 And this is just a framework! Frameworks for DecisionMaking

  17. A very useful method, best when actions, outcomes, probabilities, desirabilities: complete outcomes: uncertain probabilities: certain desirabilities: certain Otherwise, useful for doing sensitivity analysis Decision Trees

  18. Decision TreesSimple Example: Parking Meter Plug the meter - $1.75 No ticket $0.00 p = 0.12 Don't plug the meter Ticket - $15.00 1-p = 0.88

  19. Decision TreesSimple Example: Parking Meter Plug the meter - $1.75 EV = -$1.75 No ticket $0.00 p = 0.12 Don't plug the meter EV = 0.12*0.00 + 0.88*-$15.00 = -$13.20 Ticket - $15.00 1-p = 0.88

  20. Four basic assumptions for utility theory 1. With sufficient calculation an individual faced with two prospects, P1 and P2, will be able to decide whether he or she prefers prospect P1 to P2, P2 to P1, or whether he or she likes each equally well. 2. If P1 is regarded at least as well as P2, and P2 at least as well as P3, then P1 is regarded at least as well as P3. 3. If P1 is preferred to P2 which is preferred to P3, then there is a mixture of P1 and P3 which is preferred to P2, and there is a mixture of P1 and P3 over which P2 is preferred. 4. Suppose the individual prefers P1 to P2 and P3 is another prospect. Then the individual prefers a mixture of P1 and P3 to the same mixture of P2 and P3. Decision Analysis: Theory-ette

  21. Utility theory as the "logic of decision"---given your beliefs and preferences it tells you other things you should believe and prefer, if you are to be consistent. Some basic concepts Shape of the utility curve Risk aversion Risk proneness ==> Utility theory accomodates different attitudes towards risk. Example of utility or preference elicitation Decision Analysis: Theory-ette(continued)

  22. When outcomes have more than one salient aspect Example, evaluating a firm: Sales Debt Quality of its products Growth of its industry.... Example, what it takes to be a "world class competitor" (Businessweek criteria): Speed Quality Service Example: choosing a city to live in Example: choosing a job Example: designing a product Multiattribute Decisions

  23. Just about all outcomes (for interesting problems) are multiattribute Note: an alternative would be to measure everything in dollars and have a single attribute utility function on dollars. Why is or why isn't this a good idea? Basic idea: reduce many (different) aspects to a single scale. Trading off apples and oranges? On the single scale---of utility---we can take expectations, if need be. We call the different outcome aspects attributes, hence "multiattribute utility theory" or MAUT (MUT?) Multiattribute Decisions

  24. How do we combine attribute values? Simple approach, assume an additive model: U(X) = w1*u1(x1) + .... + wn*un(xn) for n attributes, where w1 + ... + wn = 1 and wi >= 0, all i Also, typically, 0 <= ui <= 1 (or 100), all i w s are "weights"---relative importance weights u s are unidimensional utility functions Accepting this simple model, our task is to represent a situation using it and to fill in the blanks AHP (analytic hierarchy process) is ONE such method. We'll look at another. Multiattribute Decisions:Combining Attribute Values

  25. Are there other ways of combining attribute values? Yes, see, e.g., Table 8.4, p. 276, in von Winterfeldt and Edwards. AHP assumes the additive model. In the AMVDSS paper, which you are to read, I used a multiplicative model in two attributes. When is it OK to use an additive model? Roughly, when the attributes are preferentially independent (OK, and usual, to be statistically dependent) Warning: this is tricky, so be careful What happens in practice? Use the additive model whenever possible and reformulate attributes to insure that's OK Multiattribute Decisions:Combining Attribute Values (con't.)

  26. From Edwards (p. 273): 1. Define alternatives and value-relevant attributes. 2. Evaluate each alternative separately on each attribute. 3. Assign relative weights to the attributes. 4. Aggregate the weights of attributes and the single-attribute evaluations of alternatives to obtain an overall evaluation of alternatives. 5. Perform sensitivity analyses and make recommendations. Different approaches differ on 2, 3, and 4. Besides agreeing on 1 and 5, all approaches rely extensively onsubjective assessments. Multiattribute Decisions:Five Universal Steps

  27. As noted, there are different versions, but here is a reasonable, workable, useful one: 1. Identify the organization whose values are to be determined. 2. Identify the purpose of the value elicitation. 3. Identify the entities (alternatives, objects) that are to be evaluated. 4. Identify the relevant dimensions of value (attributes). 5. Rank the dimensions in order of importance. 6. Make ratio estimates of the relative importance of each attribute relative to the one ranked lowest in importance. 7. Sum the importance weights; divide each by the sum. 8. Measure the relative value of each entity (alternative, object) on each dimension on a scale of 0 to 100. 9. Calculate the overall values using a weighted additive model. 10. Choose the alternative that maximizes the overall value. SMART: 10 Steps

  28. 1. Identify the organization whose values are to be determined. 2. Identify the purpose of the value elicitation. 3. Identify the entities (alternatives, objects) that are to be evaluated. Pretty obvious, but often forgotten, at the peril of the forgetters. SMART: Discussion of the 10 Steps

  29. 4. Identify the relevant dimensions of value (attributes). A useful technique: value trees. Basic idea: have gross and detailed descriptions of value, e.g., Speed Quality Service and each of these can be broken down into attributes. SMART: Discussion of the 10 Steps

  30. 5. Rank the dimensions in order of importance. This is convenient and helps to make the subjective assessment a little easier. One needn't agonize over ties or close calls. 6. Make ratio estimates of the relative importance of each attribute relative to the one ranked lowest in importance. Try this: taking into account the actual ranges assumed for the attributes, give the least important attribute 10 points. Give the next least important attribute 10 or more points..... 7. Sum the importance weights; divide each by the sum. This normalizes the wi s to a 0--1 scale. Note: a nice technique for doing sensitivity analysis in a spreadsheet. SMART: Discussion of the 10 Steps

  31. 8. Measure the relative value of each entity (alternative, object) on each dimension on a scale of 0 to 100. This is more involved that it sounds. We're after ui(xi) for each i and for each object to be evaluated. First, determine the upper and lower limits for each xi (this should have been done earlier) Determine which is best for each xi, the upper or the lower bound. Get a utility function for each xi, ui(xi). The easy thing: draw a straight line. Utility elicitation (with risk): use lotteries and midpoint splitting Value elicitation (with certainty): midpoint splitting, ask What value of x is halfway between these two extremes, measured in value to me? Now, actually do the score, get xij, j ranging across all options. Apply the utility function, ui, to each xij score SMART: Discussion of the 10 Steps

  32. 9. Calculate the overall values using a weighted additive model. 10. Choose the alternative that maximizes the overall value. These steps are easy! 9. Plug your numbers into the (additive) formula to get a value score for each alternative. 10. Pick an alternative with the highest score. ...but do sensitivity analysis! How? SMART: Discussion of the 10 Steps

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