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Multi Criteria Decision Analysis Theory

Multi Criteria Decision Analysis Theory. Fred Wenstøp. Theoretical Foundation. Von Neumann - Morgenstern's utility theory from 1944

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Multi Criteria Decision Analysis Theory

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  1. Multi Criteria Decision AnalysisTheory Fred Wenstøp Fred Wenstøp: MCDM

  2. Theoretical Foundation • Von Neumann - Morgenstern's utility theory from 1944 • A person whose preferences satisfy a set of reasonable requirements for consistency or rationality and is indifferent to the fun of gambling and does not entertain regrets • has got a utility function • maximizes expected utility when he makes decisions according to his preferences • Keeney and Raiffa's "Multi Criteria Decision Making" (MCDM) from 1976 • Structuring complex decision problems • Paying attention to several objectives at the same time • Paradigme • To help the decision maker formulate goals, weight them and making them operational Fred Wenstøp: MCDM

  3. Terminology • Criteria • operationalize the goals (objectives, ends) • Scores • the resulting values of the criteria when a decision is implemented • Weights • express the importance of the criteria and reflect the decision maker's subjective values (preferences) • Goal hierarchy (value tree) • structure of the decision maker's objectives • Option (decision alternative) • an action which influences the scores of the criteria Fred Wenstøp: MCDM

  4. The MCDM Method: Problem structuring Fred Wenstøp: MCDM

  5. The MCDM method: Model building Fred Wenstøp: MCDM

  6. Common preference models • Additive utility function • Multiplicative utility function • Multilinear utility function Fred Wenstøp: MCDM

  7. Interpretation of weights • Assume • x = salary • ux is linear ux(200) = 0 ux(600) = 1 wx= 0,4 • y = work load • uy is linear uy(60) = 0 uy(30) = 1 wy= 0,3 • z = vacation • uz is linear uz(2) = 0 uz(8) = 1 wz= 0,3 • Then • U(200,60,2) = 0 U(600,60,2) = 0,4 • The weight of a criterion is the increase in overall utility when going from a global low to the best score for that criterion. Fred Wenstøp: MCDM

  8. Assumptions • To use a multiplicative utility function: • One criterion must be utility independent of the other criteria • This means that the risk attitude with respect to this criterion is independent of the scores of the other criteria • The assumptions makes it possible to define unconditional utility functions for each individual criterion without knowing the scores of the others. • This criterion, in pair with each of the other criteria must be preference independent of the rest of the criteria • This means that the trade-offs between pairs of criteria are independent of the scores of the other criteria • The assumption makes it possible to define unconditional weights • If the sum of the weights is close to unity, an additive utility function can be used Fred Wenstøp: MCDM

  9. Utility independence • Is Salary utility independent of Work Load and Vacation? • Assume that the decision maker is indifferent between the lottery and the sure outcome in the first table • Then he must also be so with regard to the second table, and all other corresponding setups Fred Wenstøp: MCDM

  10. Preference independence • Is Salary and Work Load preference independent of Vacation? • Assume that the decision maker is indifferent between A and B in the first table • Then he must also be so with regard to the second table, and all other corresponding setups Fred Wenstøp: MCDM

  11. Completeness All important objectives are taken into account Operationality The criteria can be scored with reasonable accuracy Appraisability The criteria have a common sense relevance for the decision maker Decomposability Each criterion contributes independently to the total performance Avoid Redundancy To avoid double counting, criteria should not overlap in the sense that they express the same objectives Minimum Size The tree should be as small as possible. 10 criteria are many. Avoid Means Criteria The criteria should as far as possible reflect ends, not means Choosing a set of criteria Fred Wenstøp: MCDM

  12. Decision Analysis Steps • 1: Identify the decision maker(s) • 2: Build a goal hierachy and identify the criteria • 3: Identify the viable options • 4: For each option, score the criteria • 5: Organize the criteria and options into a decision table • 6: Determine a judgement weight for each criterion • 7: Compute the performance of each option • 8: Make a provisional decision • 9: Perform sensitivity analysis Fred Wenstøp: MCDM

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