1. 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

2. Multi Criteria Examples Facility Location Supplier Selection Equipment Purchasing Prioritizing Projects Job Applicants Evaluation Environmental Assessment

3. 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, …

4. Multi Criteria Decision Making Goal Programming Pareto optimality MAUT, Multi Attribute Utility Theory, Keeney & Raiffa Europe: Electra (Roy et al.) USA : AHP (Saaty)

5. 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

6. Pareto Optimality Not possible to improve one criteria while maintaining all others Trade-off curves, efficient frontier See Chemcon.xls and AdTradeoff.xls

7. 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

8. AHP, Pros & Cons Pros: Doable Pairwise Comparison Consistency Index Cons: AHP scale (1-9) Difficult if very many alternatives

9. 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

10. AHP Scale 1Equal 3Slightly more important 5Strongly more important 7Very strongly more important 9Absolutely more important

11. Pairwise Comparison Wi = Weight of Criteria nr. i W1/W1W1/W2W1/Wn W2/W1W2/W2W2/Wn A = Wn/W1Wn/W2Wn/Wn

12. 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

13. Pareto Efficient Frontier Grade for other Cost Alt 1 Alt 2 Alt 3 Alt 4 Alt 5