Decision Analysis Part 4: Multi-Attribute Models. Motivation for Multi-Attribute Modeling. ID s and Multiple Objectives. Questions.

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1 Decision Support: Multi-Attribute Methods Jožef Stefan International Postgraduate School,, Ljubljana Programme: Information and unication Technologies [ICT3] Course Web Page: Decision Analysis Part 4: Multi-Attribute Models Institut Jožef Stefan, Department of Knowledge Technologies, Ljubljana and University of Nova Gorica Motivation for Multi-Attribute Modeling So far we have considered single-objective models, but most of real-life decisions are multiple-objective: e.g.: price + performance (conflicting) Influence diagrams facilitate multi-objective modeling to some degree. However, is needed in terms of model development and analysis of decisions. Thus, specialised models and software. Multi-attribute modeling is very useful and practical. ID s and Multiple Objectives Invest? Return on investment Overall Satisfaction Maximize Overall Satisfaction Return on Investment Computer Industry Growth Invest in Computer Industry Venture succeeds or fails Questions Evaluation Models 1. Have you ever encountered a: multi-objective decision problem? multi-attribute model? When, where, for what kind of problems? 2. Compare multi-attribute models with: decision trees influence diagrams 3. Suggest types of decision problems suitable for the application of multi-attribute models options EVALUATION EVALUATION MODEL ANALYSIS

2 Multi-Attribute Models Multi-Attribute Models cars buying maint PRICE digital photo camera multi-attribute model functions size DIM TECH weight evaluation of cameras safety doors pers COMF TECH CAR sensor body lens COMP PHOTO lug problem decomposition 55 price quality Multi-Attribute Modelling: Why? Systematic, structured approach (to difficult real-life problems) Model development: problem decomposition into smaller, less-complex subproblems requires understanding and careful elaboration of the problem facilitates and motivates communication and knowledge interchange Evaluation: selection of a single option option ranking Analysis: what-if analysis sensitivity analysis explanation: how? (evaluation procedure) why? (selective explanation of advantages/disadvantages) option generation Contributes to better decisions: understanding, justification, explanation, documentation Multi-Attribute Model Structure F(X F(X 1,X 1,X 2,,X 2,,X n ) n ) X 1 X X n n a 1 a 2 a 3 a 1 a 2 a 3 a 1 a 2 a n YY (UTILITY) FUNCTION ATTRIBUTES OPTIONS Multi-Attribute Model for Car Selection CAR CAR Quantitative Multi-Attribute Model for Car Selection FUNCTION CAR CAR 50 P 50 P P P 3 3 F(X F(X 1,X 1,X 2,,X 2,,X n ) n ) FUNCTION 1 0 PRICE PRICE FUEL FUEL SAFETY ATTRIBUTES PRICE PRICE FUEL FUEL SAFETY a 1 a 2 a 3 a 1 a 2 a 3 a 1 a 2 a n CARS OPTIONS

3 Qualitative Multi-Attribute Model for Car Selection FUNCTION (DECISION RULES) high high high high un un un un low low low low un un un un high high low low un un med med high high un un med med med med med med med med low low low low low low med med med med low low low low low low CAR CAR Hierarchical Multi-Attribute Model X6 F(X1,X2,X3) Y F(X6,X4,X5) utility value (utility) utility value function function aggregate aggregate attributes attributes utility value function function PRICE PRICE FUEL FUEL SAFETY X1 X2 X3 X4 X5 basic basic attributes attributes med med high high high high low low low low med med un un un un a1 a2 a3 a4 a5 alternative alternative (option) OPTIONS Multi-Attribute Modelling: Why? Systematic, structured approach (to difficult real-life problems) Model development: problem decomposition into smaller, less-complex subproblems requires understanding and careful elaboration of the problem facilitates and motivates communication and knowledge interchange Evaluation: selection of a single option option ranking Analysis: what-if analysis sensitivity analysis explanation: how? (evaluation procedure) why? (selective explanation of advantages/disadvantages) option generation Contributes to better decisions: understanding, justification, explanation, documentation Multi-Attribute Modelling: How? 0. Problem identification 1. Tree (or hierarchy) of attributes 2. Utility functions 3. Evaluation and analysis of alternatives 4+ Implementation 1. Tree of Attributes Decomposition of the problem to to sub-problems ("Divide and Conquer!") 2. Utility Functions (Aggregation) Aggregation: bottom-up aggregation of attributes values CAR CAR CAR CAR PRICE TECH.CHAR. PRICE 75% 25% TECH.CHAR. BUYING MAINTEN SAFETY COMFORT BUYING MAINTEN SAFETY COMFORT The most difficult stage! SAFETY COMFORT TECH.CH. low exc un high low un med ept ept high exc

4 3. Evaluation and Analysis 3. Evaluation and Analysis buying EVALUATION direction: bottom-up (terminal root attributes) result: each option evaluated inacurate/uncertain data? buying ANALYSIS interactive inspection what-if analysis sensitivity analysis explanation maint PRICE maint PRICE safety safety CAR CAR doors TECH doors TECH pers COMF pers COMF lug lug MADM Tools Spreadsheet Modelling 1. Paper and Pencil (Abacon) 2. Spreadsheets and mathematical modelling software(ms Excel) 3. Specialized MADM software Specialized Software (1/4) Logical Decisions Criterium DecisionPlus Specialized Software (2/4) t Choice HiView WinPre Downloadables/winpre.html

5 Specialized Software (3/4) Specialized Software (4/4) Web-HIPRE DEX Vredana DEXi Exercise You would like to buy a new laptop computer for your own purposes (study, internet, fun,...). Suggest a suitable set of attributes and create a tree of attributes. Consider the guidelines presented on the next two slides. Developing Attribute Structure Three basic strategies: Top-Down: Start with the overall evaluation (target objective), decompose it to sub-goals. Bottom-Up: Start with desirable characteristics, subgoals. Group them into connected, meaningful sub-trees. Middle-Out: Combining the two above. Iteratively decompose (refine) and group (generalise) attributes. Developing Attribute Structure Desirable features of attributes and their structure: Completeness: Do not overlook important attributes Relevance (non-redundancy): Use only relevant attributes, omit redundant attributes Minimality: Use a minimal number of attributes Orthogonality: Basic attributes should be independent of each other Operativity: Basic attributes should be easy to assess or measure Comprehensibility: Create meaningful sub-trees of interrelated attributes Working Example One Thursday morning, Charles, instead of attending his Management Science Techniques for Consultants class, was mulling over his four job offers. His offers came from: Acme Manufacturing, Bankers Bank, Creative Consulting, and Dynamic Decision Making. He knew that factors such as,, amount of management science (which he loved), and long term prospects were important to him, but he wanted some way to formalize the relative importance, and some way to evaluate each job offer. Adapted from: Michael A. Trick, Analytic Hierarchy Process,

6 Kepner-Tregoe Kepner-Tregoe Model Kepner, C. H., Tregoe, B. B. (1981). The New Rational Manager. Princeton Research Press. Characteristics: list of attributes importance of attributes is expressed by weights [0,10] alternatives are described by vectors of values [0,10] evaluation (aggregation) principle: weighted sum supported analyses: what-if, sensitivity Job Offers Method: Kepner-Tregoe alternative A B C D attribute weight value w*v value w*v value w*v value w*v management science long-term prospects total Kepner-Tregoe Tregoe: : What-If Analysis Kepner-Tregoe Model: Charts Job Offers long-term prospects Weights long-term prospects; 3 Weights ; 2 Method: Kepner-Tregoe alternative C original C - C2 attribute weight value w*v value w*v value w*v management science long-term prospects total Attributes management science Va lue s management science; 5 Attribute Values ; long-term prospects management science Value Attribute A B V alue Stano vanje A B C D Kepner-Tregoe Tregoe: : Sensitivity Analysis AHP 140 Sensitivity analysis AHP: Analytic Hierarchy Process (Thomas Saaty, 1980) Value A B C D Characteristics: based on multiple attribute hierarchies assessing weights by a pairwise comparison of attributes assessing preferences by a pairwise comparison of alternatives consistency analysis Weight of

7 Hierarchy of Attributes Pairwise Comparison Values (BASIC) ATTRIBUTES JOB MS WEIGHTS long PREFERENCES 1 Items i and j are of equal importance (preference) 3 Item i is weakly important (better) than j 5 Item i is strongly important (better) than j 7 Item i is very strongly important (better) than j 9 Item i is absolutely important (better) than j 2,4,6,8 are intermediate values ALTERNATIVES Acme Bankers Creative Dynamic Assessing Weights Assessing Preferences (Scores) For each attribute, e.g., Location, compare alternatives: 1. Normalize the columns so that the sum equals 1 2. Take the average of rows. 1. Normalize the columns so that the sum equals 1 2. Take the average of rows. Assessing Preferences (Scores) Scores for all the attributes: AHP Software Criterium DecisionPlus t Choice Evaluation: Acme: Banks: Creative:.335 Dynamic:.238 WinPre Downloadables/winpre.html

8 Web-HIPRE Software Web-HIPRE Homework 1. Run Web-HIPRE 2. Load one of the existing models (e.g., Cellular Phone) 3. Look at all Web-HIPRE s features for describing alternatives assessing alternatives preferences and scores assessing attributes weights 4. Do the following: evaluation of alternatives sensitivity analysis 5. Try to make some changes to the model: structure, preferences, weights (but no need to save) DEX: t System Shell for Multi-Attribute Decision Making , DOS DEXi: DEX for ion Computer Program for Multi-Attribute Decision Making 1999, Windows DEX and DEXi: : Background 1. Multi-Attribute Decision Making modelling using criteria and utility functions problem decomposition and structuring option evaluation and analysis 2. t Systems qualitative (symbolic) variables "if-then" decision rules decision model = knowledge base emphasis on the explanation of results (DEX) DEXi Computer Program for Multi-Attribute Decision Making A simple computer program for MADM that facilitates: Creation and editing of model structure (tree of attributes) value scales of attributes decision rules (incl. using weights) options and their descriptions (data) Evaluation of options (can handle missing values) Presentation of evaluation results with: tables charts Analyses: what-if, ±1, selective explanation, comparison Preparing reports and charts DEXi Model Attribute Scale Job un; ; ; exc un; ; un; ; satisfaction un; ; MS un; ; long un; ; Tables satisfaction Job 33% 33% 33% 1 un * * un 2 * un * un 3 * * un un 4 >= 5 >= 6 >= exc MS long satisfaction 50% 50% 1 un * un 2 * un un 3 4 >= 5 >=

9 DEXi Evaluation Evaluation results B Attribute A B C D Job un un un un un satisfaction un MS un long un satisfaction satisfaction D satisfaction satisfaction Stages of MADM with DEXi 0. Problem Identification a. problem formulation b. formation of a decision-making group c. selection of decision-support methodology 1. Identification of Attributes a. unstructured list of attributes b. hierarchy (tree) of attributes c. measurement scales 2. Definition of Utility Functions (Decision Rules) 3. Evaluation and Analysis of Options a. description of options (data acquisition) b. evaluation of options c. analysis 4. Implementation Stages of MADM (with DEXi) 0. Problem Identification a. problem formulation b. formation of a decision-making group c. selection of decision-support methodology 1. Identification of Attributes a. unstructured list of attributes b. hierarchy (tree) of attributes knowledge acquisition c. measurement scales 2. Definition of Utility Functions (Decision Rules) 3. Evaluation and Analysis of Options a. description of options (data acquisition) b. evaluation of options c. analysis 4. Implementation DECOMPOSITION AGGREGATION EXPLOITATION 1.a: Unstructured List of Attributes Problem in Personnel Management: Select of a Candidate for a Job (e.g., a project manager) education age experience references knowledge work approach ability to work in a group Do not overlook important attributes! leadership organizational abilities loyalty intelligence communicativity character health 1.b: Tree of Attributes Create meaningful, related groups Avoid aggregate attributes having than three descendants

10 1.b: Tree of Attributes 1.c: Scales un,,, exc un,, un,, un,, prim/sec, high, univ, MSc, PhD no, pas, act none, to1year, 1-5, 6-8, 18-20, 21-25, 26-40, 41-55, poor, aver,, exc D, C, B, A less, approp, Scales are discrete, typically ordered from bad to Values should distinguish between importantly different characteristics Their number should gradually increase from bottom to the root 1.c: Scales 2: Decision rules Utility Functions, Bottom-Up Aggregation poor poor poor aver aver aver less approp less approp Abilit un un un un exc less approp less un un exc exc approp 2: Decision rules 3.a: Description of Options Candidate Age Test A MSc pas to1year B B PhD act aver less B

11 3.a: Description of Options 3.bc: Evaluation and Analysis of Options 1. Evaluation proceeds from bottom (basic attributes) to the root result: qualitative evaluation of each option handles missing (DEXi) or imprecise (DEX) option values 2. Analysis interactive inspection of results what-if analysis analyses: compare options ±1 analysis selective explanation reports charts 3.b: Evaluation of an Option 3.b: Evaluation of Options Candidate A MSc pas to1year B 3.c: What-If Analysis 3.c: What-If Analysis Candidate A no effect Candidate A exc MSc PhD pas to1year B MSc pas to1year B act

12 3.c: What-If Analysis 3.c: ±1 Analysis 3.c: Compare options 3.c: Selective Explanation Candidate B un un un PhD act B aver less 3.c: Selective Explanation Charts and Reports

13 DEX and DEXi: ience Wide applicability to various application areas Usually, solutions are specific (non-general) 1. Model development time heavily problem-dependent: from hours to months typical: 2 to 15 days 2. The most difficult stage designing the tree of attributes 3. Appropriate decision problems many attributes (> 15) many options (> 10) prevailing qualitative decision-making, judgment inurate or missing data group decision making (communication and explanation) sufficient resources available (expertise, time) DEX in DEXi: Future Combined qualitative and quantitative models Extensions: Data Mining (e.g. machine learning of models by HINT) Data Bases, Data Warehouses, OLAP Software: Dex Machine : Low-level OO library for QQ models Various types and levels of GUI DEX and DEXi: Summary 1. Combination of multi-attribute decision making and expert systems 2. Characteristics: qualitative (symbolic) decision making explanation and analysis active support in the acquisition of decision rules 3. Applicability: for complex real-world problems over 50 real-life applications Exercise 1. Take one of the already defined empty models shown on the next slide 2. Define all utility functions (decision rules) in that model 3. Define and describe a few (about 4) options 4. Evaluate and analyse the options 5. Extend the model: add and/or refine a few attributes (including their scales and rules) repeat the steps 2, and Prepare and print out (or save) a report Models Portable Computer Attribute Description PORTABLE Portable computer COMMERCIAL PRICE [ in Euro ] IMAGE TECHNICAL INTERNAL PROCESSOR MEMORY DISK EXTERNAL MONITOR KEYBOARD AUTONOMY Car Selection Attribute Description CAR Quality of a car PRICE Price of a car BUY.PRICE Buying price MAINT.PRICE Maintenance price TECH.CHAR. Technical characteristics COMFORT Comfort #PERS Maximum number of passengers #DOORS Number of doors LUGGAGE Size of the luggage boot SAFETY Car's safety Programmer s Performance Attribute Description PROGRAMMER Programmer's Performance KNOWLEDGE Knowledge of the Programmer EXPER Working ience SPECIAL Specialized Knowledge WORK Quality of Programmer's Work QUALITY Quality of the Results EFFECTIVE Work Effectivenes: Are the results delivered in time? APPROACH Working Approach TEAM Attitude to Team Work PERSONAL Characteristics INITIATIVE Self Initiativeness CREATIVE Creativity Performance Evaluation of Companies Attribute Description ENTERP Performance evaluation of enterprises FINANC RETURN PROFIT PROF-AB LIQUID ECONOMIC PRODUCT CAPACITY Also available: