Multicriteria Decision Aid: the Outranking Approach Multicriteria decision

Multicriteria Decision Aid: the Outranking Approach Multicriteria decision

Multicriteria Decision Aid: the Outranking Approach Multicriteria decision aid PROMETHEE & GAIA methods Decision Lab software March 2008 Bertrand Mareschal ULB SMG & Solvay Business School [email protected] 1 http://homepages.ulb.ac.be/ Course summary 1. Unicriterion vs. multicriteria models. 2. Multicriteria modeling: Basic concepts. 3. Multi-attribute utility theory (aggregation US school). 4. Outranking methods (French school). 5. PROMETHEE & GAIA methods. 6. Decision Lab software iVision project. March 2008 2 Decision making Real world Social Political

Economical Industrial Environmental Military Describe, Understand, Manage. 2 Approaches : Qualitative approach, Quantitative approach. March 2008 3 Decision aid Ralit Real world Sociale Social Politique Political Economique Economical Industrielle Industrial Environnementale Environmental Militaire Military

Quantitative model Possible decisions? How to compare them? Preferences, Objectives? March 2008 4 Decision aid Ralit Real world Sociale Social Politique Political Economique Economical Industrielle Industrial Environnementale Environmental Militaire Military Quantitative model Approximation to real world! Decision aid. March 2008 5

Some Decision or Evaluation Problems Locating a new plant, a new shop, ... Human resources management. Purchasing equipment. Assessing the quality of suppliers. Evaluating projects. Selecting an investment strategy. March 2008 6 Unicriterion vs multicriteria model Unicriterion model: Optimise g (a) a A Mathematically well-stated: Optimal solution, Complete ranking of the actions. Socio-economically ill-stated: Single criterion? Not realistic. Notion of criterion: perception thresholds, March 2008 7

Unicriterion vs multicriteria model Multicriteria model: Optimise g1 ( a), g 2 (a),..., g k ( a) a A Mathematically ill-stated: No optimal solution, No mathematical meaning. Socio-economically well-stated: Closer to real world decision problem, Search for a compromise solution. March 2008 8 of multicriteria decision aid 1968 : ELECTRE I method (B. Roy) 1972 : 1st international conference in the USA 1973 : 1st ULB thesis on MCDA 1975 : European working group 1977 : Charnes & Cooper: The main impetus for the burst of new applications seems to be associated with the evolution of public management science and its very natural orientation towards

multiobjective formulation. 1980-85 : 12% of papers in European conferences. 1992 : international journal JMCDA March 2008 9 Multicriteria table Actions: Possible decisions, items to evaluate. Criteria: quantitative, qualitative. March 2008 10 Multicriteria table Crit. Crit. 1 Crit. 2 Crit. 3 4 (/20)

(rating) (qual.) (Y/N) Action 1 Action 2 Action 3 Action March4 2008 18 135 G Yes 9 147 B

Yes 15 129 VG No 12 146 VB ? 11 Plant location Environm. (BEF) Costs (BEF)

(impact) Site 1 18 135 G Site 2 9 147 B Site 3 15 129 VG

Site 4 12 146 VB Site 5 7 121 G Investment

March 2008 12 Purchase options Price (BEF) Reliability (days) Maintenanc e (estimate) Product A 18 135 G Product B 9

147 B Product C 15 129 VG Product March D 2008 12 146 VB 13 A simple example Purchase of a car Objectives :

Economy (price), Usage (fuel consumption), Performance (power), Space, Comfort. March 2008 14 Multicriteria table Car Tour. A Sport Tour. B Lux. 1 Economic Lux. 2 Price 360000 390000 355000 480000 250000 450000 Power Consumpt. 75 8,0 110 9,0 7,0

85 90 8,5 50 7,5 85 9,0 Space A VB G G B VG Comfort A B A VG VB G Best buy? Best compromise? Priorities of buyer? March 2008 15 Modeling 1 2 3 2.

Define the criteria 1. Define the actions March 2008 g1 g2 g3 a g 1(a ) g 2(a ) g 3(a ) b g 1(b )g 2(b )g 3(b ) c 3. Model the preferenc es 16 Defining the actions Definition : Let A the set of actions. A can be defined:

by extension: by enumeration of its elements. relatively small number of actions. by comprehension: by constraints on a set of decision variables. (Cf. linear programming) large number or infinity of actions. March 2008 17 Some properties of the set of actions A can be: stable: a priori defined, doesnt evolve. evolutive: can evolve during the procedure. globalised: mutually exclusive elements. fragmented: combinations of actions are considered. March 2008 18 Defining the criteria Definition: function g defined on A, taking its values in

a totally ordered set, and representing an objective of the decision-maker. Consistent family of criteria: Include all aspects of the decision problem, all the objectives of the decision-maker, Avoid redundancies. March 2008 19 Qualitative criteria Qualitative scales: Maximum 9 levels (7 2) to ensure a consistent evaluation. Presence of a neutral level? Examples: Very good, Good, Average, Bad, Very bad Yes, No ++, +, 0, -, - ++, +, -, -- Underlying numerical scale (coding).

March 2008 20 Modeling preferences Problem: How to compare two actions a and b to each other? A first model: 3 possible results: 1. 2. 3. March 2008 Preference: Indifference: Incomparability: aPb or bPa aIb aRb 21 Preference structures Properties (logical): aPb not bPa aIa P is asymetrical aIb bIa

I is symetrical Not aRa R is non-reflexive aRb bRa R is symetrical I is reflexive P, I and R define a preference structure if, for all a,b in A, one and only one of the following statements holds: aPb or bPa or aIb or aRb March 2008 22 Traditional preference structure (unicriterion) Optimisation of a function g on A aPb g a g b a, b A : aIb g a g b Consequences: R is empty P is transitive I is transitive Complete ranking.

March 2008 23 The notion of indifference threshold Problem: Indifference can be intransitive. Cf. Coffee cup paradox (Luce, 1956) Introduction of an indifference threshold: aPb a, b A : aIb g a g b q g a g b q Quasi-order : P is transitive, but not I. March 2008 24 Other preference structures Variable indifference threshold Interval order. Preference + indifference thresholds Pseudo-order. Models including incomparability Partial orders. Valued preference structures.

March 2008 25 Social choice theory Problem: A group of voters have to select a candidate among a group of candidates (election). Each voter has a personal ranking of the candidates according to his/her preferences. Which candidate must be elected? What is the best voting procedure? Analogy with multicriteria decision aid: Candidates actions, Voters criteria. March 2008 26 5 procedures among many others 1. Relative majority.

2. Condorcet. 3. Second ballot (French presidential). 4. Borda. 5. Successive eliminations. March 2008 27 Procedure 1 : Relative majority 3 candidates: Albert, voters: Bruno,30Claire 11 10 9 voters voters voters A B C

B C B C A A A 11 B 10 C 9 Albert is elected March 2008 28 Procedure 1 : Relative majority 3 candidates: Albert,

voters: Bruno,30Claire 11 10 9 voters voters voters A B C B C B C A A

March 2008 A 11 B 10 C 9 Problem: B and C preferred Albert is elected to A by a majority of 29 voters! Marie Jean Antoine Nicolas de Caritat Marquis de Condorcet 1743 - 1794 March 2008 30 Procedure 2 : Condorcet 3 candidates: Albert, voters: Bruno,30Claire

11 10 9 voters voters voters A B C B C A C B A B preferred to A B preferred to C C preferred to A 19

votes 21 votes 19 votes Bruno is elected March 2008 31 Procedure 2 : Condorcet paradox 3 candidates: Albert, voters: Bruno,9 Claire 4 3 2 voters voters voters A B

C March 2008 B C A C A B A preferred to B B preferred to C C preferred to A Nobody is 6 votes 7 votes 5 votes 32 Procedure 3 : second ballot (French presidential election)

4 candidates: Albert, Bruno, 63 Diane voters: Claire, 22 21 20 voters voters voters B C D A A A C D

C D B B March 2008 1st tour: B and C C beats 2nd tour: B (41 vs 22) Claire is elected 33 Procedure 3 : second ballot (French presidential election) 4 candidates: Albert, Bruno, 63 Diane voters: Claire, 22 21 20

voters voters voters B C D A C D March 2008 A D B A C B Claire is elected ...but !!! A preferred to C A preferred to B

A preferred to D 42 votes 41 votes 43 votes 34 Procedure 3 : second ballot (French presidential election) 3 candidates: Albert, voters: Bruno,17Claire 5 6 4 2 voter s voter s

voter s voter s C A B B A B C A B C A C March 2008

1st tour: A and B A beats 2 B (11 vs tour: 6) Albert is elected nd 35 Procedure 3 : second ballot (French presidential election) 3 candidates: Albert, voters: Bruno,17Claire 5 6 4 2 voter s voter

s voter s voter s C A B A B C A B BA B C A C Albert was

elected 1st tour: A and C 2nd tour: C bat A (9 contre 8) Claire is elected ! Problem: non-monotonicity! March 2008 36 Jean Charles de Borda 1733 - 1799 March 2008 37 Procedure 4 : Borda 31 x 2 + 39 x 1

11 x 2 + 11 x 1 3 candidates: Albert, voters: Bruno,81Claire 30 29 10 10 1 1 vote rs vote rs vote rs vote rs vote r

vote r Poin ts A C C B A B 2 C A B A B C

1 B B A C C A 0 Claire is March 2008 elected! Scores A 10 1 B 33 C

10 9 39 x 2 + 31 38 x 1 Procedure 4 : Borda 3 candidates: Albert, voters: Bruno,81Claire 30 29 10 10 1 1 vote rs vote rs vote rs

vote rs vote r vote r Poin ts A C C B A B 2 C A B A

B C 1 B B A C C A 0 March 2008 A preferred to C : 41 on 81 Scores A 10 1

B 33 C 10 9 39 Procedure 4 : Borda 4 candidates: Albert, Bruno, 7 voters: Claire, Diane 3 2 2 vote rs vote rs vote rs C

B A B A D March 2008 A D C Scores Points 3 D 2 C B 1 0 Albert is elected Ranking

A 13 A B 12 B C 11 C D 6 D 40 Procedure 4 : Borda 4 candidates: Albert, Bruno, 7 voters: Claire, Diane 3

2 2 vote rs vote rs vote rs C B A B A C A C B Scores Points 2 1 0 Ranking

A 6 C B 7 B C 8 A Claire is elected March 2008 41 Borda (manipulation) 3 candidates: Albert, Bruno, Claire34 voters: 12 12

10 Scores Points vote vote Brunos partisans rs rs generate the 2 A B C candidacy of1x ( B A A fake candidate ) vote rs C C B 0 Ranking

A 46 A B 36 B C 20 C Albert is elected March 2008 42 Borda (manipulation) 4 candidates: Albert, Bruno, 34 x voters: Claire, Scores 12

12 10 vote rs vote rs vote rs A B C B x A 2 B x 1

C x March 2008 A C Points 3 0 Bruno is elected! Ranking A 68 B B 70 A C 42

C x 24 x 43 Borda (manipulation) 4 candidates: Albert, Bruno, 34 x voters: Claire, Scores 12 12 10 vote rs vote rs vote rs A

B C x x x 2 A B 1 B C A C Points 3 0 The fake candidate is elected! March 2008

Ranking A 58 x B 48 A C 30 B x 68 C 44 Procedure 5 : Eliminations successives Tour-wise procedure. Principle: Eliminate progressively the worst candidates, one by one, until only

one is left. March 2008 45 Conclusion? 5 candidates: Albert, Bruno, Claire, voters: Diane,25Eric Relative majority Albert 8 7 4 4 2 elected Second ballot: voter voter voter voter voter s s s s s Bruno elected Condorcet: A B E

D C C D C E D C D B B E B C E A A

A March 2008 Claire E elected Borda: Diane D elected Successive eliminations B Eric elected A 46 Kenneth Arrow (Nobel prize in economy, 1972) Impossibility theorem (1952): With at least 2 voters and 3 candidates, it is impossible to build a voting procedure that simultaneously satisfies the 5 following properties:

Non-dictatorship. Universality. Independence with respect to third parties. Monotonicity. Non-imposition. March 2008 47 Problematics g1 g2 g3 a g 1(a ) g 2(a ) g 3(a ) b g 1(b )g 2(b )g 3(b ) c Evaluations n actions k criteria - choice: determine a subset of actions

(the best ones ). - sorting: sort actions in predefined categories. - ranking: rank from the best to the worst action. - description: describe actions and their consequences. March 2008 48 Dominance and efficiency Objective . Based on a unanimity principle: a dominates b g h (a) g h (b) h Efficiency: a is efficient if it is not dominated by any other action. Problems: Dominance is poor (few dominances), Many actions are efficient. March 2008 49 Objections to dominance I

g1 g2 II 10 10 0 0 ab efficient 20 30 a a a preferred to b March 2008 g1 g2 III 10 0 a b b and20

30 a 10 0 IV efficient a and b g1 incomp. g2 V a a 10 99 0 ab and99 b 10 efficient 0 a and b g1 g2 10 99 0

b a and 20b 10 efficient 0 a preferred to g1 b g2 10 0 10 0 ab efficient 99 99 a and b indiffer. 50 Some characteristics for a good multicriteria method Take into account deviations between evaluations. Take scale effects into account. Build either a partial (P,I,R) or a complete (P,I) ranking of the actions. Stay sufficiently simple:

no black box, no technical parameters. March 2008 51 A common approach: The weighted sum Actions or Decisions Criteria g1 g2 g3 a g 1(a ) g 2(a ) g 3(a ) b g 1(b )g 2(b )g 3(b ) c w1 w2 w3

Weights of the criteria March 2008 52 A common approach: The weighted sum Global value for a : V(a) = w1 g1(a) + w2 g2(a) + a is preferred to b if: V(a) > V(b) (if all criteria are to maximise) March 2008 53 Weighted sum: Example 1 a b g1 g2 g3 g4 g5

100 85 1/5 100 85 1/5 100 85 1/5 100 85 1/5 55 100 1/5 V(a) = 91 V(b) = 88 Total and uncontrolled compensation of weaknesses by strengthes. March 2008 54 Weighted sum: Example 2 a b c

d g1 g2 100 0 50 50 1/2 0 100 50 50 1/2 V(a) = V(b) = V(c) = V(d) = 50 Elimination of conflicts Loss of information. March 2008 55 Weighted sum: Example 3 Profit is approximately 2 times more important than time savings; 0.7 for profit and 0.3 for time savings. a b

March 2008 g 1 (BF) g 2 (min) 60 48 0.7 60 70 0.3 V(a) = 60 V(b) = 54.6 a is ranked 1st. 56 Weighted sum: Example 3 Profit is approximately 2 times more important than time savings; 0.7 for profit and 0.3 for time savings. a b March 2008 g 1 (FF) g 2 (min)

10 8 0.7 60 70 0.3 V(a) = 25 V(b) = 26.6 b is ranked 1st! 57 Weighted sum: Example 3 a b a b g 1 (BF) g 2 (min) 60 48 0.7 60 70 0.3

g 1 (FF) g 2 (min) 10 8 0.7 60 70 0.3 V(a) = 60 V(b) = 54.6 a is ranked 1st. V(a) = 25 V(b) = 26.6 b is ranked 1st. Significance of weights ! March 2008 58 Multicriteria decision aid Multiattribute utility theory (US school). Outranking methods (French school). Interactive methods. Multiobjective programming. Since 1970, numerous developments:

conferences, papers, books, applications, software... March 2008 59 Multiattribute utility (MAUT) Single synthesis criterion (aggregation). U a U g1 a , g 2 a , , g k a Existence? Construction? Mathematical form? k U a U g a j j additive? j 1

March 2008 60 Multiattribute utility (MAUT) Mode of construction : direct, indirect. Information intensive for the decision maker. (quantity of information vs reliability?). Not flexible (sensitivity analyses). Far away from the original decision problem structure: multicriteria unicriterion March 2008 61 Outranking methods Majority principle (vs unanimity for dominance). Pairwise comparison of actions. Closer to the decision problem. ELECTRE methods (1968-). PROMETHEE & GAIA methods (1983-). March 2008

62 Different approaches ing Outrank Unicriterion approach Weighted sum Pairwise comparisons Foundation Mathematical Economical Economical Compensatio n between criteria - Total

Limited Scales - Linked to weigths of criteria Taken into account Conflict detection - No Yes March 2008 63 Decision aid methods Supplementary information: Perception of scales Weighing of criteria Analysis Procedure:

Prescriptive approach: PROMETHEE Descriptive approach: GAIA March 2008 64 Comparison of 2 actions Crit. Crit. 1 Crit. 2 Crit. 3 4 (/20) (rating) (qual.) (Y/N) Action 1 Action 2 Action 3 Action March4 2008 B Oui= 6 Difference 18

135 9 147 M Oui 15 129 TB Non 12 146 TM ?

65 Preference function Preference degree 1 Difference 0 Q Indifference threshold March 2008 6 P Linear Preference threshold 66 PROMETHEE Pref (Eco.,Lux.) 1,0 0,0 0,5 0,0 0,0

Pref (Lux.,Eco.) Economic -230000 Price 250000 Power 50 -1,0 Consumpt. 7,5 Space B Comfort VB Preference Deviation March 2008 Lux. 1 480000 90 8,5 G VG +40 +2 +4

0,0 1,0 0,0 0,5 1,0 Wght 1 1 1 1 1 Pref (Eco.,Lux.) = 0,3 = (1 + 0 + 0,5 + 0 + 0 ) / 5 Pref (Lux.,Eco.) = 0,5 67 PROMETHEE Pref (Eco.,Lux.) 1,0 0,0 0,5 0,0 0,0 Pref (Lux.,Eco.) Economic -230000 Price

250000 Power 50 -1,0 Consumpt. 7,5 Space B Comfort VB Preference +40 +2 +4 0,0 1,0 0,0 0,5 1,0 Wght 2 1 2 1 1 Pref (Eco.,Lux.) = 0,43 = (2 x 1 + 0 + 2 x 0,5 + 0 + 0 ) / 7 Pref (Lux.,Eco.) = 0,36

= (0 + 1 + 0 + 0,5 + 1 ) / 7 Deviation March 2008 Lux. 1 480000 90 8,5 G VG 68 Pairwise comparisons For each criterion gj : Preference function Pj Weight wj Multicriteria preference degree of a over b : k a, b w j Pj a, b j 1

March 2008 69 Preference functions (as in Decision Lab software) Q Usual Q P Level March 2008 P U shape Q P Linear V shape S Gaussian

70 PROMETHEE Pref (Eco.,Lux.) Economic -230000 Price 250000 Power 50 -1,0 Consumpt. 7,5 Space B Comfort VB 1,0 0,0 0,5 0,0 0,0 Lux. 1 480000 90 8,5 G VG Pref (Lux.,Eco.) +40

+2 +4 0,0 1,0 0,0 0,5 1,0 Preference Deviation March 2008 Pairwise comparisons 71 Pairwise preference matrix (a,b) a, b Tour. A Sport Tour.B Lux.1 Econ. Lux.2 a Tour. A 0,00 Sport 0,00 Tour.B 0,00 Lux.1 0,00 0, 50 Econ. 0,30 0,00 Lux.2 0,00 a

a March 2008 72 Pairwise preference matrix (a,b) a, b Tour. A Sport Tour.B Lux.1 Econ. Lux.2 a Tour. A 0,00 0,34 0,00 0, 21 0, 26 0, 22 Sport 0,20 0,00 0,16 0, 24 0,30 0, 24 Tour.B 0,15 0,55 0,00 0,32 0, 45 0,33 Lux.1 0,18 0, 45 0,10 0,00 0,50 0,15 Econ. 0, 20 0,34 0,14 0,30 0,00 0,35 Lux.2 0, 24 0,30 0,10 0,04 0,60 0,00 a a

March 2008 73 Computation of preference flows a, b Tour. A Sport Tour.B Lux.1 Econ. Lux.2 a Tour. A 0,00 0,34 0,00 0, 21 0, 26 0, 22 0, 21 Sport 0,20 0,00 0,16 0, 24 0,30 0, 24 0, 23 Tour.B 0,15 0,55 0,00 0,32 0, 45 0,33 0,36 Lux.1 0,18 0, 45 0,10 0,00 0,50 0,15 0, 28 Econ. 0, 20 0,34 0,14 0,30 0,00 0, 35 0, 27 Lux.2 0, 24 0,30 0,10 0,04 0,60 0,00 0, 26 a 0,19 0, 40 0,10 0, 22 0, 42 0, 26 a 0,02 -0,17

0,26 0,06 -0,15 0,00 March 2008 74 Preference flows b b (a) (a) a Leaving flow: (strength) Entering flow: (weakness) Net flow: March 2008 a 1 (a)

a, b n 1 bA 1 (a ) b, a n 1 bA (a) (a) (a) 75 PROMETHEE Rank decisions from the best to the worst ones. Identify best compromise solutions. March 2008 76 PROMETHEE PROMETHEE I : partial ranking PROMETHEE II : complete ranking March 2008

, 77 Properties of the net flow Net flow is centered: a 0 a A Unicriterion net flows: k a w a j j j 1 with 1 a P a, b P b, a n 1 j March 2008 j

bA j 78 Outranking and rank reversal Pairwise comparisons (outranking) not transitive due to the multicriteria nature of the decision problems: a , b b, a b, c c , b a, c c, a Rank reversals unavoidable to obtain a transitive ranking (preorder). March 2008 79 Rank reversals in PROMETHEE Limited: Net flow is the least squares optimal score with respect to rank reversal.

Centered score s(a) that minimizes: Q s a s b a, b b, a a March 2008 b 80 2 GAIA 1. Computation of unicriterion net flows (normalization) 2. Projection on a plane: Graphical representation. 5 dimensions! March 2008 81 GAIA Discover conflicts among criteria. Identify potential

compromises. Help to fix priorities. March 2008 82 GAIA Actions: points Criteria: axes March 2008 = 90% 83 GAIA Price Economic: 15 k Tourism: 25,5-26 k Sport: 29 k Luxury: 35-38 k = 90% March 2008 84

GAIA Power Sport: 110 kW Luxury: 85-90 kW Tourism: 75-85 kW Economic: 50 kW = 90% March 2008 85 GAIA PROMETHEE II ! Tour.B : Actions: 0,26 points Lux.1 : 0,06 : Tour.A 0,02Criteria: Lux.2axes : 0,00 Econ. : -0,15

March 2008 = 90% 86 GAIA Actions: points Criteria: axes March 2008 = 90%!! only % information !! 87 PROMETHEE & GAIA methods PROMETHEE : prescriptive approach Partial ranking (prudent) - PROMETHEE I Complete ranking (rating) - PROMETHEE II

GAIA : descriptive approach Identification of conflicts among criteria. Profiles of actions. Fix priorities, sensitivity analysis (decision axis). March 2008 88 Home assignment Set up a decision problem (up to 60 cells): min. 5 actions and 5 criteria. Model the problem in Decision Lab. Analyze the problem, including weight sensitivity analysis. Produce a written report including: Problem description, Preference modeling choices (scales, preference functions, weights), Complete PROMETHEE & GAIA analysis results, Conclusion.

Max. 20 pages including figures. March 2008 89 Example 2 : Plant location Actions: Criteria: 5 potential sites g1 : Cost (investment) g2 : Cost (operations) g3 : Employment g4 : Transportation g5 : Environmental impact

g6 : Social impact March 2008 90 Evaluation table Criteria to minimize or maximize. Different scales. March 2008 Quantitative or qualitative criteria. 91 Mono- and Multi-decision maker decision problems Mono-decision maker : Single stakeholder (decision maker). Single evaluation table and preference structure. Multi-decision maker:

Multiple stakeholders (including decision maker(s)). Multiple evaluation tables and preference structures. Looking for a consensus solution. March 2008 92 Example 2 Four stakeholders (decision makers): Industrial (actual decision maker), Political authorities (regional), Environmental protection groups, Workers unions (social). Four multicriteria tables. March 2008 93 Multicriteria matrix Adapt multicriteria methods to multidecision maker problems. Analyze conflicts

among decision makers. Help to achieve consensus solution. March 2008 94 Multi-scenarios model Scenarios: Points of view, Hypotheses, Evaluations: Objective criteria: common evaluations. Subjective criteria: specific evaluations for each scenario. Specific preference structures : Weights, preference thresholds. March 2008

95 Multi-scenarios model Adaptation of PROMETHEE: Individual rankings. Global (group) rankings taking into account a possible weighing of the scenarios. Adaptation of GAIA: Two distinct analyses. March 2008 96 Individual views Single scenario: (fixed decision maker) PROMETHEE rankings Classical monodecision maker GAIA plane: March 2008 Axes = criteria

Points = actions 97 Multi-scenarios synthesis Aggregating all scenarios (group). PROMETHEE group rankings. Classical GAIACriteria plane: March 2008 Axes = criteria Points = actions 98 GAIA-Criteria plane Information: C2 A4 A2 C1 C4 A3

Pertinence: C3 March 2008 Conflicts among criteria. For mostly objective criteria. A1 99 Multicriteria synthesis Aggregating all criteria. (group) Global PROMETHEE rankings. GAIA-scenarios plane: March 2008 Axes = decision makers Points = actions 100

GAIA-Scenarios plane Information: D 2 A4 A2 D1 D4 A3 Origin of conflicts? D3 March 2008 Global view of conflicts among scenarios (decision makers). A1

Definition of criteria, Subjective criteria, Definition of actions, Individual priorities. 101 March 2008 102 Group decision making Up to 80% of upper management and executives working time spent in meetings. Time consuming (meetings, travel), High cost. Limited efficiency of classical meetings: Limited time allocated to each participant, Psychological restraints, Limited memory, Important stakes for organisations. March 2008

103 GDSS Rooms March 2008 104 Group Decision Support System Use IT to improve the efficiency of meetings. Electronic brainstorming. Working in parallel. Possible anonymity. Automated report generation. Decision Aid. Voting procedures. GDSS rooms or Internet. Time savings and costs reduction. March 2008 105 Some applications at SMG Financial evaluation of companies.

Quality assesment of suppliers. Electricity production planning at Electrabel. Regional planning. Evaluation of urban waste management syst ems . Environmental applications. Therapeutical choice. ... March 2008 106 Decision Lab 2000 PROMETHEE & GAIA software http://homepages.ulb.ac.be/~bmaresc/ disk1.htm Data management: Qualitative scales, Categories of actions or criteria. PROMETHEE I et II GAIA Sensitivity analysis tools: Walking weights, Stability intervals.

Multiple scenarios (GDSS) March 2008 107 iVision project New software. New visual tools: Visual interactive preference modeling. Representation of PROMETHEE rankings. GAIA extensions: GAIA-stick GAIA-criterion March 2008 108

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