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Executive Manager. Decision Making and Policy Planning, typically with many goals Sometimes even > 1 decision maker (Game Theory, Group Decisions) Linear Programming with many goals -> Goal Programming Also decision problems that are not LP -> MCDM methods. Multi Criteria Examples.
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Executive Manager • Decision Making and Policy Planning, typically with many goals • Sometimes even > 1 decision maker (Game Theory, Group Decisions) • Linear Programming with many goals -> Goal Programming • Also decision problems that are not LP -> MCDM methods
Multi Criteria Examples • Facility Location • Supplier Selection • Equipment Purchasing • Prioritizing Projects • Job Applicants Evaluation • Environmental Assessment
EQI for Icelandic Power Plants • Versatility, Uniqueness, Size, International Importance, Informational Value: • Cultural • Ecosystems • Animal & Plant Species • Earth & Water systems • Geology, waste untouched areas • Outdoor activities, tourism, farming, …
Multi Criteria Decision Making • Goal Programming • Pareto optimality • MAUT, Multi Attribute Utility Theory, Keeney & Raiffa • Europe: Electra (Roy et al.) • USA : AHP (Saaty)
Goal Programming, GP • LP model with many objective functions • See AdGoals.xls in chapter 9 in W&A • Soft vs Hard Constraints • Deviation Variables • Priorities, Preemptive Optimization • Weights on Criteria
Pareto Optimality • Not possible to improve one criteria while maintaining all others • Trade-off curves, efficient frontier • See Chemcon.xls and AdTradeoff.xls
Analytic Hierarchy Process • Thomas Saaty 1975 • Expert Choice Software (www.expertchoice.com) • >1500 books and papers on AHP • Case Studies Collection • See Solver3.xls (Facility Location) and AHPJobs.xls in chapter 9
AHP, Pros & Cons • Pros: • Doable • Pairwise Comparison • Consistency Index • Cons: • AHP scale (1-9) • Difficult if very many alternatives
AHP method • 1. Pairwise Comparison of Criteria => Weights of Criteria. Check Consistency. • 2. Pairwise Comparison of Alternatives against each criteria => grading. Check Consistency. • 3. Final grade calculated from weights and grading for each criteria. Sensitivity Analysis
AHP Scale • 1 Equal • 3 Slightly more important • 5 Strongly more important • 7 Very strongly more important • 9 Absolutely more important
Pairwise Comparison • Wi = Weight of Criteria nr. i W1/W1 W1/W2 W1/Wn W2/W1 W2/W2 W2/Wn A = • Wn/W1 Wn/W2 Wn/Wn
Consistency Check • 1. Calculate A*w’ • 2. M = (1/n)*i(A*w’)i/w’i • 3. CI = (M – n)/(n – 1) • 4. CI/RI > 0,1 => Inconsistency • Where: n = 2 3 4 5 6 7 8 • => RI = 0 0,58 0,90 1,12 1,24 1,32 1,41
Pareto Efficient Frontier Cost Alt 2 Alt 5 Alt 3 Alt 4 Alt 1 Grade for other