FEB 622 MULTICRITERIA DECISION ANALYSIS Multicriteria Decision Making
FEB 622: MULTICRITERIA DECISION ANALYSIS
Multicriteria Decision Making • Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is used to evaluate multiple conflicting criteria in decision making • MCDM is helps with structuring and solving decision and planning problems involving multiple criteria. • The purpose is to support decision-makers facing alternative decision problems. • Typically, there does not exist a unique optimal solution for multiplecriteria decision problems • Decision-maker's preferences is often used to differentiate between solutions.
Components of MCDA problems • Goal • Decision maker or group of decision makers with opinions (preferences) • Decision alternatives • Evaluation criteria (interests) • Outcomes or consequences associated with alternative/interest combination
Steps in MCDA • Step 1: Define the Decision Opportunity • Step 2: Identify Stakeholder Interests • Step 3: Build a Decision Framework • Step 4: Rate the Alternatives • Step 5: Weight Stakeholder Interests • Step 6: Score the Alternatives • Step 7: Discuss Results, Re-Score, Discuss Again, Decide
Methods for solving MCDM Problems • Weighted sum model (WSM) • Weighted product model (WPM) • Analytic Hierarchy Process (AHP) • Elimination and Choice Translating Reality (ELECTRE) • Technique for Order Preference by Similarly to Ideal Solution (TOPSIS) • Fuzzy AHP Method
Modelling MCDA: Analytical Hierarchy Process • Step 1: Set up the goal • Step 2: Set up/determine evaluation criteria • Step 3: Develop/outline comparison matrix • Step 4: Calculate priority vector • Step 5: Assess goodness of fit
Example: Find suitability for groundwater borehole • Step 1: Goal – to find suitable site for locating groundwater borehole • Step 2: Identify alternatives FACTOR Proximity Slope Geology Land use SCALED SCORE Suitable Moderate Slight Not Suitable Site A 2 1 3 3 1 2 3 4 Site B 1 2 4 1 Site C 3 2 2 1 Site D 4 3 2 3
Example: Find suitability for groundwater borehole • Step 3: Develop pairwise comparison table Proximilty Slope Proximilty 1 Slope 2 1 Geology 0. 333 0. 5 Land use 0. 5 2 Geology 1 4 Land use 1
Example: Find suitability for groundwater borehole • Step 4: Calculate Root of product Proximity Slope Geology Land use Proximity 1 2 0. 333333 0. 5 Slope 0. 5 1 0. 5 2 Geology 3 2 1 4 Land use Root of product 2 0. 75 0. 25 0. 0105 1 1 Sum = 2. 260
Example: Find suitability for groundwater borehole • Step 5: Calculate priority vector (priority weights) Proximity Slope Proximity 1 0. 5 Slope 2 1 Geology 0. 333333 0. 5 Land use 0. 5 2 Geology Land use Root of product Priority Vector 3 2 0. 75 0. 331797 2 0. 5 0. 221198 1 0. 25 0. 0105 0. 004608 4 1 1 0. 442396 Sum = 2. 260 Sum=1
Example: Find suitability for groundwater borehole • Step 6: Assess for goodness of fit Proximity Slope Geology Land use Sum*PV Proximity 1 2 0. 333333 0. 5 Slope 0. 5 1 0. 5 2 Geology 3 2 1 4 Land use Root of product Priority Vector 2 0. 75 0. 331797 0. 5 0. 221198 0. 25 0. 0105 0. 004608 1 1 0. 442396 Sum = 2. 260 Sum=1 3. 833333 4 10 3. 75 1. 271889 0. 884793 0. 046083 1. 658986 max = 3. 862 • Consistency Index (CI) = ( max – n)/(n-1) = -0. 0461
Example: Find suitability for groundwater borehole • Step 6: Assess for goodness of fit • Consistency Index (CI) = ( max – n)/(n-1) = -0. 0461 • Consistency Ration (CR) = CI/Random Index (Criteria: CR <=10% for consistent decision – good fit) • CR {for n = 4, RI = 0. 9} = - 0. 05 (< 10% so OK)
Example: Find suitability for groundwater borehole • Step 7: Calculate suitability Initial Scores Suitability calculations Site A Site B Site C Site D Site A Proximilty 2 1 3 4 0. 664 0. 332 0. 995 1. 327 Slope 1 2 2 3 0. 221 0. 442 0. 664 Geology 3 4 2 2 0. 014 0. 018 0. 009 Land use 3 1 1 3 1. 327 0. 442 1. 327 2. 226 1. 235 1. 889 3. 327 Rank Suitability 3 Slight Site B 1 Site C 2 Site D 4 Suitable Moderate Not Suitable
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