Decision Trees and Influence Diagrams
|
|
- Kenneth Rose
- 6 years ago
- Views:
Transcription
1 29/10/15 Decision Trees and Influence Diagrams Carlos Bana e Costa and Mónica Oliveira REFERENCES: CLEMEN, R. (1996), MAKING HARD DECISIONS: AN INTRODUCTION TO DECISION ANALYSIS (2 ND EDITION). DUXBURY. CHAPTERS 3, 4, AND 12 GOODWIN, P. AND WRIGHT, G. (1998) DECISION ANALYSIS FOR MANAGEMENT JUDGMENT (2 ND OR 3 RD EDITIONS). WILEY. CHAPTERS 6 AND 8 Lecture topics q Decision trees and influence diagrams q Value of informa4on and control q A case study: Drilling for oil q Payoff matrix q Complementary concepts 2 1
2 A Taxonomy of Decision Models (In Decision Analysis in the 1990s - L.D. Phillips) Problem dominated by Uncertainty MulRple ObjecRves EXTEND conversaron Event tree Fault tree Influence diagram REVISE opinion Bayesian nets CHOOSE opron Payoff matrix Decision tree EVALUATE oprons MulR-criteria decision analysis ALLOCATE resources MulR-criteria commons dilemma SEPARATE into components Credence decomposiron Risk analysis NEGOTIATE MulR-criteria bargaining analysis 3 Dealing with uncertainty: Key ques]ons? What are the key uncertain)es? What are the possible outcomes of these uncertain4es? What are the chances of occurrence of each possible outcome? What are the consequences of each outcome? Hammond, Keeney & Raiffa, Smart Choices (Chapter 7) 4 2
3 Decision problem: To drill or not to drill? q A small and struggling firm has the mineral rights to a tract of land. A consultant geologist esrmates there is a small chance of striking oil. q It is expensive to drill for oil, and the cost of drilling if there is no oil will nearly drive the firm to bankruptcy. q On the other hand, if they strike oil, the firm will make a big killing. q There is another alternarve: a rival firm has offered to buy the land. 5 What are the key uncertain)es? Uncertainty: To strike oil (by drilling) What are the possible outcomes of this uncertainty? Oil No oil (Dry) What are the chances of occurrence of each possible outcome? There is a small chance of striking oil (There is a high chance that the soil is dry) What are the consequences of each outcome? If they strike oil, the firm will make a big killing If there is no oil it will nearly drive the firm to bankruptcy 6 3
4 Risk profile Uncertainty: To strike oil in the site (by drilling) Outcome Chance Consequences Oil Small Big profit No oil (dry) High Bankruptcy 7 Decision table What are the chances of occurrence of each possible outcome? 8 4
5 Decision tables (and Decision Trees): Most classical approach to model decision problems involving sequencial decisions under uncertainty: q The idea underlying a tabular representaron of a problem is that the consequences of any decision can be determined by a number of external factors, out of the control of the DM. q If the DM knew the state of nature that would actually hold, the true state, he could predict the consequence of his choice with certain. (Note: The true state is unknown, but the DM knows which states are possible.) 9 Decision tree Decision nodes Represent decisions Chance nodes Represent chance (uncertain) events Consequences are specified at the ends of the branches 10 5
6 A DECISION TREE represents all of the possible paths that the DM might follow through Rme, including all possible decision alternarves and outcomes of chance events: The oprons represented by branches from a decision node must be such that the DM can choose only one op9on. Each chance node must have branches that correspond to a set of mutually exclusive and collec9vely exhaus9ve outcomes When the uncertainty is resolved, one and only one of the outcomes occurs 11 If a chance node is to the right of a decision node, the decision must be made in an9cipa9on of the chance event. Conversely, placing a chance event before a decision means that the decision is made condi9onal on the specific chance outcome having occurred. Imperfect informaron: DM waits for informaron before making a decision most attractive least attractive Asymmetric tree with sequenral decisions The crescent shape indicates that the uncertain event may result in any value between two limits. 12 6
7 DPL sobware 13 NODES: Influence diagrams Decision nodes (rectangles) - represent decisions (and alternarves) Chance nodes (ovals) represent uncertain events (and outcomes) (chance events) Consequence (and calcula4on) nodes represent consequences (and calcularons) Nodes are put together in a graph, connected by ARCS. Arcs represent rela9onships (relevance or sequence) between nodes: Predecessor node à successor node (Done with DPL sohware) 14 7
8 Using PrecisionTree 1.0 for Excel to solve the problem (Trial available at Palisade website Student version available with Clemen & Reilly, 2001) (PrecisionTree disrnguishes calcularon nodes from pay-off nodes) 15 Oil Dry EMV (Expected Monetary Value) Drill = 0.25(700)+0.75(-100) Sell Prior probability Highest (EMV): Choose Drill 16 8
9 Indifference point Drill Sell 0.25: a priori probability 17 Supposing that the geologist is clairvoyant EVPI = =
10 Case study: Drilling for oil (con]nua]on: Obtaining imperfect informa]on) However, another opron prior to making a decision is to follow the geologist s suggesron of conducrng a detailed seismic survey of the land, to obtain a bemer esrmate of the probability of finding oil. The cost of the survey is 30,000. Since EVPI=142.5 (the maximum amount that the DM should be willing to pay the clairvoyant for perfect informa4on) far exceeds 30, it may be worthwhile to proceed with the seismic survey and wait for its results before making a decision. NOTE: We are thinking about the value of informaron in a strictly a priori sense. The geologist is not a clairvoyant, unfortunately! I.e., the results of the survey can be imperfect. 19 q The value of informaron tells you the value of finding out the state of a chance event before you have to make a decision. q Chance events with high values for informa4on present the best opportunires to improve your expected value by thinking of crearve new alternarves. q Chance events with low values for informa4on are probably not worth further efforts at research, tesrng, or delay. Important things to remember: InformaRon has no value if it doesn t change your acrons, Its value is limited to the improvement it provides over what you would get without it
11 21 Case study: Drilling for oil (con]nua]on: Obtaining imperfect informa]on) A seismic survey obtains seismic soundings that indicate whether the geological structure is favourable to the presence of oil. Based upon past experience, our DM got the informaron that: If the land is dry, the surveys are unfavourable 80% of the Rme. However, if there is oil, the surveys are favourable only 60% of the Rme
12 Case study: Drilling for oil (con]nua]on: Obtaining imperfect informa]on) What we know 0.25* * * * What we know: 0.25*0.6 What we want to know: P(O\F)=? Oil Underground P(D\F)=? P(O\U)=? Oil Underground P(D\U)=? 24 12
13 What we want to know: P(O\F)=1/2 =.15/.30 Oil Underground P(D\F)=.15/.30 P(O\U)=.1/.7 Oil Underground P(D\U)=.6/.7 Posterior probabili4es (Bayes rule) 25 backward induc4on procedure (rollback) EMV for wairng for the survey results = 153 EMV for deciding without survey = 100 Expected value of imperfect informaron (EVII) = =53 (>30) (The DM would never want to pay more than 53,000 for the survey) Make the survey. If favourable, drill. If unfavourable, sell
14 Value of control Some variables, such as weather, have high informaron value but are hard to think of good sources of informaron for. For these variables, move on to the value of control to see if you can think of ways to mirgate the impact of these uncertainres, even if you can t predict them. The value of control for an event tells you the value of being able to choose the outcome of the uncertainty rather than taking your chances. The value comes from being able to guarantee the most favourable outcome and prevent less favourable outcomes. 27 Most favourable outcome Value of control = =
15 Chance Events with High Value of Control present the greatest opportunity for improving your outcomes by thinking of crea4ve new ways to either gain control over the uncertainty or to mi4gate its impact on your outcomes. Common sources of control: q Increased staffing, Rme, money, or other resources q PR or adverrsing q Insurance As with informaron, sources of control are rarely free. Those whose cost is less than their benefit should be modelled explicitly in your influence diagram and decision tree. Common types of imperfect control: q Control just improves probabilires. q Can t pick best state. 29 Important things to remember about the value of control: q it can come either from controlling the underlying uncertainty or by insularng yourself from the effects of that uncertainty; q the value of control is normally greater than, or equal to, the value of informaron
16 CHOOSE op]on decision tree Graham s decision problem Speed Flexibility Accuracy Cost Weights: Assess the Cash Flows and probabili]es using the Precision Tree sobware 32 16
17 Precision Tree (PALISADE) Examples 33 Decision Trees vs. Influence Diagrams Influence Diagrams Strengths Compact Good for communicaron, in parrcular in the structuring phase Good overview of large problems Good for understanding the relevance between uncertainty nodes Decision Trees Displays details, being good for in-depth understanding Flexible representaron Best for asymmetric decision problems Adequate for performing sensirvity analysis Weaknesses Details suppressed Becomes very messy for large problems Complementary use of decision trees and influence diagrams! 34 17
18 Forecast Hits Miami Misses Miami Developing Influence Diagrams: Some examples Outcomes Hits Miami Misses Miami Alterna4ves Evacuate Stay Source: Clemen, R. (1996), Making Hard Decisions: An IntroducRon to Decision Analysis (2nd EdiRon). Duxbury. Choice Outcome Conseq. risk Conseq. cost Evacuate Hits Miami Low risk High cost Misses Miami Low risk High cost Stay Hits Miami High risk High cost Misses Miami Low risk Low cost 35 But if there is missing informa]on: The case for sequen]al decisions... Source: Clemen, R. (1996), Making Hard Decisions: An IntroducRon to Decision Analysis (2nd EdiRon). Duxbury
19 More on sequen]al decisions... Source: Clemen, R. (1996), Making Hard Decisions: An IntroducRon to Decision Analysis (2nd EdiRon). Duxbury. 37 Developing financial models while accoun]ng for uncertainty 1 st version 3 rd version 2 nd version Source: Clemen, R. (1996), Making Hard Decisions: An IntroducRon to Decision Analysis (2nd EdiRon). Duxbury
20 PAYOFF TABLE 39 Depar]ng from a Payoff Table with informa]on for making a choice under uncertainty Some situarons in which there is uncertainty, but no probabilisrc informaron Several strategies Several scenarios Example Table with Net Present Value (NPV) from different investment strategies and scenarios: Strategy Scenario C1 Scenario C2 Scenario C3 S S S
21 Algorithms to make Choices under Uncertainty A ) Laplace ( principle of insufficient reason ) B ) Wald (Pessimist - Maximin) C ) MaxiMax (OpRmist) D ) Hurwicks (Intermediate) E) Savage ( MiniMax Regret ) 41 A ) LAPLACE principle of insufficient reason Equiprobable E[NPVs,S1] = ( )/3 = 800/3 E[NPVs,S2] = ( )/3 = 625/3 E[NPVs,S3] = ( )/3 = 540/3 B ) WALD Pessimist - Maximin min (S1) = 100 min (S2) = 150 min (S3) = 160 Choose S1 Strategy Scenario C1 Scenario C2 Scenario C3 S S S Maximin = 160 Choose S
22 C ) MaxiMax Op4mist Strategy Scenario C1 Scenario C2 Scenario C3 S S S Max (S1) = 500 Max (S2) = 300 Max (S3) = 200 MaxiMax = 500 Choose S1 D ) Hurwicks Op4mism coefficient - α (between 0 and 1), weighted average of the extremes à Ex: α = 0.7 S = 380 S = 255 S = 188 Choose S1 (380) 43 Strategy Scenario C1 Scenario C2 Scenario C3 S S S E) SAVAGE ( MiniMax Regret - Minimize maximum regret) Regret Matrix Strategy Scenario C1 Scenario C2 Scenario C3 S Max = 60 S Max = 200 S Max = 300 minimax 60 à Choose S
23 Complementary concepts EXPECTED MONETARY VALUE RISK PROFILE 45 The Risk Profile concept A risk profile is a graph that shows the chances associated with possible consequences. Probability Risk Profile For Oil Diagram of oil_infl.xls 0,6 0,5 0,4 0,3 0,2 0, Value Each risk profile is associated with a strategy, a parrcular immediate alternarve, as well as specific alternarves in future decisions
24 The Cumula]ve Risk Profile concept q In this format, the verrcal axis is the chance that the payoff is less than or equal to the corresponding value on the horizontal axis. q It results from adding up, or accumularng the chances of the individual payoffs à Along the horizontal axis we can read the chance that the payoff will be less than or equal to that specific value. 1,2 Cumulative Probability For Oil Diagram of oil_infl.xls Cumulative Probability 1 0,8 0,6 0,4 0,2 F(y) = P(Y y) = P(Y = i) i:i y Value 47 The Expected Value concept The random variable Y has many possible outcomes! Expected value: BEST GUESS for Y, what number would you give? Ε Y n = y i p i [ ] = y i P(Y = y i ) i=1 i=1 n Interpreta4on: If you were able to observe many outcomes of Y, the calculated average of all the outcomes would be close to E[Y]
A Taxonomy of Decision Models
Decision Trees and Influence Diagrams Prof. Carlos Bana e Costa Lecture topics: Decision trees and influence diagrams Value of information and control A case study: Drilling for oil References: Clemen,
More informationModule 15 July 28, 2014
Module 15 July 28, 2014 General Approach to Decision Making Many Uses: Capacity Planning Product/Service Design Equipment Selection Location Planning Others Typically Used for Decisions Characterized by
More informationChapter 18 Student Lecture Notes 18-1
Chapter 18 Student Lecture Notes 18-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 18 Introduction to Decision Analysis 5 Prentice-Hall, Inc. Chap 18-1 Chapter Goals After completing
More informationDecision Analysis. Chapter Topics
Decision Analysis Chapter Topics Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility Decision Analysis
More informationDecision Making Models
Decision Making Models Prof. Yongwon Seo (seoyw@cau.ac.kr) College of Business Administration, CAU Decision Theory Decision theory problems are characterized by the following: A list of alternatives. A
More informationSubject : Computer Science. Paper: Machine Learning. Module: Decision Theory and Bayesian Decision Theory. Module No: CS/ML/10.
e-pg Pathshala Subject : Computer Science Paper: Machine Learning Module: Decision Theory and Bayesian Decision Theory Module No: CS/ML/0 Quadrant I e-text Welcome to the e-pg Pathshala Lecture Series
More informationDecision Making. D.K.Sharma
Decision Making D.K.Sharma 1 Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision
More informationDecision Analysis Models
Decision Analysis Models 1 Outline Decision Analysis Models Decision Making Under Ignorance and Risk Expected Value of Perfect Information Decision Trees Incorporating New Information Expected Value of
More informationDecision Analysis. Chapter Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall
Decision Analysis Chapter 12 12-1 Chapter Topics Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility
More informationDecision Making Supplement A
Decision Making Supplement A Break-Even Analysis Break-even analysis is used to compare processes by finding the volume at which two different processes have equal total costs. Break-even point is the
More informationDecision Making. DKSharma
Decision Making DKSharma Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision making
More informationDecision Analysis CHAPTER LEARNING OBJECTIVES CHAPTER OUTLINE. After completing this chapter, students will be able to:
CHAPTER 3 Decision Analysis LEARNING OBJECTIVES After completing this chapter, students will be able to: 1. List the steps of the decision-making process. 2. Describe the types of decision-making environments.
More informationDecision Support Models 2012/2013
Risk Analysis Decision Support Models 2012/2013 Bibliography: Goodwin, P. and Wright, G. (2003) Decision Analysis for Management Judgment, John Wiley and Sons (chapter 7) Clemen, R.T. and Reilly, T. (2003).
More informationChapter 13 Decision Analysis
Problem Formulation Chapter 13 Decision Analysis Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information
More informationProject Risk Evaluation and Management Exercises (Part II, Chapters 4, 5, 6 and 7)
Project Risk Evaluation and Management Exercises (Part II, Chapters 4, 5, 6 and 7) Chapter II.4 Exercise 1 Explain in your own words the role that data can play in the development of models of uncertainty
More informationCauses of Poor Decisions
Lecture 7: Decision Analysis Decision process Decision tree analysis The Decision Process Specify objectives and the criteria for making a choice Develop alternatives Analyze and compare alternatives Select
More informationNext Year s Demand -Alternatives- Low High Do nothing Expand Subcontract 40 70
Lesson 04 Decision Making Solutions Solved Problem #1: see text book Solved Problem #2: see textbook Solved Problem #3: see textbook Solved Problem #6: (costs) see textbook #1: A small building contractor
More informationAgenda. Lecture 2. Decision Analysis. Key Characteristics. Terminology. Structuring Decision Problems
Agenda Lecture 2 Theory >Introduction to Making > Making Without Probabilities > Making With Probabilities >Expected Value of Perfect Information >Next Class 1 2 Analysis >Techniques used to make decisions
More information1.The 6 steps of the decision process are:
1.The 6 steps of the decision process are: a. Clearly define the problem Discussion and the factors that Questions influence it. b. Develop specific and measurable objectives. c. Develop a model. d. Evaluate
More informationSCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT. BF360 Operations Research
SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT BF360 Operations Research Unit 5 Moses Mwale e-mail: moses.mwale@ictar.ac.zm BF360 Operations Research Contents Unit 5: Decision Analysis 3 5.1 Components
More informationMBF1413 Quantitative Methods
MBF1413 Quantitative Methods Prepared by Dr Khairul Anuar 4: Decision Analysis Part 1 www.notes638.wordpress.com 1. Problem Formulation a. Influence Diagrams b. Payoffs c. Decision Trees Content 2. Decision
More informationProject Risk Analysis and Management Exercises (Part II, Chapters 6, 7)
Project Risk Analysis and Management Exercises (Part II, Chapters 6, 7) Chapter II.6 Exercise 1 For the decision tree in Figure 1, assume Chance Events E and F are independent. a) Draw the appropriate
More informationINTERNATIONAL UNIVERSITY OF JAPAN Public Management and Policy Analysis Program Graduate School of International Relations
Hun Myoung Park (5/2/2018) Decision Analysis: 1 INTERNATIONAL UNIVERSITY OF JAPAN Public Management and Policy Analysis Program Graduate School of International Relations DCC5350/ADC5005 (2 Credits) Public
More informationESD.71 Engineering Systems Analysis for Design
ESD.71 Engineering Systems Analysis for Design Assignment 4 Solution November 18, 2003 15.1 Money Bags Call Bag A the bag with $640 and Bag B the one with $280. Also, denote the probabilities: P (A) =
More informationChapter 3. Decision Analysis. Learning Objectives
Chapter 3 Decision Analysis To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Learning Objectives After completing
More informationDecision Making. BUS 735: Business Decision Making and Research. exercises. Assess what we have learned. 2 Decision Making Without Probabilities
Making BUS 735: Business Making and Research 1 1.1 Goals and Agenda Goals and Agenda Learning Objective Learn how to make decisions with uncertainty, without using probabilities. Practice what we learn.
More informationDecision Making. BUS 735: Business Decision Making and Research. Learn how to conduct regression analysis with a dummy independent variable.
Making BUS 735: Business Making and Research 1 Goals of this section Specific goals: Learn how to conduct regression analysis with a dummy independent variable. Learning objectives: LO5: Be able to use
More informationDECISION ANALYSIS. (Hillier & Lieberman Introduction to Operations Research, 8 th edition)
DECISION ANALYSIS (Hillier & Lieberman Introduction to Operations Research, 8 th edition) Introduction Decision often must be made in uncertain environments Examples: Manufacturer introducing a new product
More informationDecision Analysis. Chapter 12. Chapter Topics. Decision Analysis Components of Decision Making. Decision Analysis Overview
Chapter Topics Components of Decision Making with Additional Information Chapter 12 Utility 12-1 12-2 Overview Components of Decision Making A state of nature is an actual event that may occur in the future.
More informationUNIT 5 DECISION MAKING
UNIT 5 DECISION MAKING This unit: UNDER UNCERTAINTY Discusses the techniques to deal with uncertainties 1 INTRODUCTION Few decisions in construction industry are made with certainty. Need to look at: The
More informationIX. Decision Theory. A. Basic Definitions
IX. Decision Theory Techniques used to find optimal solutions in situations where a decision maker is faced with several alternatives (Actions) and an uncertain or risk-filled future (Events or States
More informationEVPI = EMV(Info) - EMV(A) = = This decision tree model is saved in the Excel file Problem 12.2.xls.
1...1 EMV() = 7...6.1 1 EMV() = 6. 6 Perfect Information EMV(Info) = 8. =.1 = 1. =.6 =.1 EVPI = EMV(Info) - EMV() = 8. - 7. = 1.. This decision tree model is saved in the Excel file Problem 1..xls. 1.3.
More informationDECISION ANALYSIS. Decision often must be made in uncertain environments. Examples:
DECISION ANALYSIS Introduction Decision often must be made in uncertain environments. Examples: Manufacturer introducing a new product in the marketplace. Government contractor bidding on a new contract.
More information- Economic Climate Country Decline Stable Improve South Korea Philippines Mexico
1) Micro-comp is a Toronto based manufacturer of personal computers. It is planning to build a new manufacturing and distribution facility in South Korea, Philippines, or Mexico. The profit (in $ millions)
More informationWhat do Coin Tosses and Decision Making under Uncertainty, have in common?
What do Coin Tosses and Decision Making under Uncertainty, have in common? J. Rene van Dorp (GW) Presentation EMSE 1001 October 27, 2017 Presented by: J. Rene van Dorp 10/26/2017 1 About René van Dorp
More informationDECISION ANALYSIS: INTRODUCTION. Métodos Cuantitativos M. En C. Eduardo Bustos Farias 1
DECISION ANALYSIS: INTRODUCTION Cuantitativos M. En C. Eduardo Bustos Farias 1 Agenda Decision analysis in general Structuring decision problems Decision making under uncertainty - without probability
More informationA B C D E F 1 PAYOFF TABLE 2. States of Nature
Chapter Decision Analysis Problem Formulation Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information Computing
More informationDecision making under uncertainty
Decision making under uncertainty 1 Outline 1. Components of decision making 2. Criteria for decision making 3. Utility theory 4. Decision trees 5. Posterior probabilities using Bayes rule 6. The Monty
More informationChapter 2 supplement. Decision Analysis
Chapter 2 supplement At the operational level hundreds of decisions are made in order to achieve local outcomes that contribute to the achievement of the company's overall strategic goal. These local outcomes
More informationTIm 206 Lecture notes Decision Analysis
TIm 206 Lecture notes Decision Analysis Instructor: Kevin Ross 2005 Scribes: Geoff Ryder, Chris George, Lewis N 2010 Scribe: Aaron Michelony 1 Decision Analysis: A Framework for Rational Decision- Making
More informationLearning Objectives = = where X i is the i t h outcome of a decision, p i is the probability of the i t h
Learning Objectives After reading Chapter 15 and working the problems for Chapter 15 in the textbook and in this Workbook, you should be able to: Distinguish between decision making under uncertainty and
More informationChapter 12. Decision Analysis
Page 1 of 80 Chapter 12. Decision Analysis [Page 514] [Page 515] In the previous chapters dealing with linear programming, models were formulated and solved in order to aid the manager in making a decision.
More information36106 Managerial Decision Modeling Decision Analysis in Excel
36106 Managerial Decision Modeling Decision Analysis in Excel Kipp Martin University of Chicago Booth School of Business October 19, 2017 Reading and Excel Files Reading: Powell and Baker: Sections 13.1,
More informationDECISION MAKING. Decision making under conditions of uncertainty
DECISION MAKING Decision making under conditions of uncertainty Set of States of nature: S 1,..., S j,..., S n Set of decision alternatives: d 1,...,d i,...,d m The outcome of the decision C ij depends
More informationIntroduction LEARNING OBJECTIVES. The Six Steps in Decision Making. Thompson Lumber Company. Thompson Lumber Company
Valua%on and pricing (November 5, 2013) Lecture 4 Decision making (part 1) Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com LEARNING OBJECTIVES 1. List the steps of the decision-making
More informationTextbook: pp Chapter 3: Decision Analysis
1 Textbook: pp. 81-128 Chapter 3: Decision Analysis 2 Learning Objectives After completing this chapter, students will be able to: List the steps of the decision-making process. Describe the types of decision-making
More informationDecision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques
1 Decision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques Thompson Lumber is looking at marketing a new product storage sheds. Mr. Thompson has identified three decision options (alternatives)
More informationM G T 2251 Management Science. Exam 3
M G T 2251 Management Science Exam 3 Professor Chang November 8, 2012 Your Name (Print): ID#: Read each question carefully before you answer. Work at a steady pace, and you should have ample time to finish.
More informationDecision Analysis under Uncertainty. Christopher Grigoriou Executive MBA/HEC Lausanne
Decision Analysis under Uncertainty Christopher Grigoriou Executive MBA/HEC Lausanne 2007-2008 2008 Introduction Examples of decision making under uncertainty in the business world; => Trade-off between
More informationOctober 9. The problem of ties (i.e., = ) will not matter here because it will occur with probability
October 9 Example 30 (1.1, p.331: A bargaining breakdown) There are two people, J and K. J has an asset that he would like to sell to K. J s reservation value is 2 (i.e., he profits only if he sells it
More information19 Decision Making. Expected Monetary Value Expected Opportunity Loss Return-to-Risk Ratio Decision Making with Sample Information
19 Decision Making USING STATISTICS @ The Reliable Fund 19.1 Payoff Tables and Decision Trees 19.2 Criteria for Decision Making Maximax Payoff Maximin Payoff Expected Monetary Value Expected Opportunity
More information56:171 Operations Research Midterm Examination Solutions PART ONE
56:171 Operations Research Midterm Examination Solutions Fall 1997 Write your name on the first page, and initial the other pages. Answer both questions of Part One, and 4 (out of 5) problems from Part
More informationThe Course So Far. Decision Making in Deterministic Domains. Decision Making in Uncertain Domains. Next: Decision Making in Uncertain Domains
The Course So Far Decision Making in Deterministic Domains search planning Decision Making in Uncertain Domains Uncertainty: adversarial Minimax Next: Decision Making in Uncertain Domains Uncertainty:
More informationDecision Analysis. Introduction. Job Counseling
Decision Analysis Max, min, minimax, maximin, maximax, minimin All good cat names! 1 Introduction Models provide insight and understanding We make decisions Decision making is difficult because: future
More informationMaking Choices. Making Choices CHAPTER FALL ENCE 627 Decision Analysis for Engineering. Making Hard Decision. Third Edition
CHAPTER Duxbury Thomson Learning Making Hard Decision Making Choices Third Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering 4b FALL 23 By Dr. Ibrahim. Assakkaf
More informationLecture 12: Introduction to reasoning under uncertainty. Actions and Consequences
Lecture 12: Introduction to reasoning under uncertainty Preferences Utility functions Maximizing expected utility Value of information Bandit problems and the exploration-exploitation trade-off COMP-424,
More informationEnergy and public Policies
Energy and public Policies Decision making under uncertainty Contents of class #1 Page 1 1. Decision Criteria a. Dominated decisions b. Maxmin Criterion c. Maximax Criterion d. Minimax Regret Criterion
More informationstake and attain maximum profitability. Therefore, it s judicious to employ the best practices in
1 2 Success or failure of any undertaking mainly lies with the decisions made in every step of the undertaking. When it comes to business the main goal would be to maximize shareholders stake and attain
More informationFull file at CHAPTER 3 Decision Analysis
CHAPTER 3 Decision Analysis TRUE/FALSE 3.1 Expected Monetary Value (EMV) is the average or expected monetary outcome of a decision if it can be repeated a large number of times. 3.2 Expected Monetary Value
More information56:171 Operations Research Midterm Examination October 28, 1997 PART ONE
56:171 Operations Research Midterm Examination October 28, 1997 Write your name on the first page, and initial the other pages. Answer both questions of Part One, and 4 (out of 5) problems from Part Two.
More informationDecision Theory. Mário S. Alvim Information Theory DCC-UFMG (2018/02)
Decision Theory Mário S. Alvim (msalvim@dcc.ufmg.br) Information Theory DCC-UFMG (2018/02) Mário S. Alvim (msalvim@dcc.ufmg.br) Decision Theory DCC-UFMG (2018/02) 1 / 34 Decision Theory Decision theory
More informationCEC login. Student Details Name SOLUTIONS
Student Details Name SOLUTIONS CEC login Instructions You have roughly 1 minute per point, so schedule your time accordingly. There is only one correct answer per question. Good luck! Question 1. Searching
More informationFW544: Sensitivity analysis and estimating the value of information
FW544: Sensitivity analysis and estimating the value of information During the previous laboratories, we learned how to build influence diagrams for estimating the outcomes of management actions and how
More informationThe Course So Far. Atomic agent: uninformed, informed, local Specific KR languages
The Course So Far Traditional AI: Deterministic single agent domains Atomic agent: uninformed, informed, local Specific KR languages Constraint Satisfaction Logic and Satisfiability STRIPS for Classical
More informationApplying Risk Theory to Game Theory Tristan Barnett. Abstract
Applying Risk Theory to Game Theory Tristan Barnett Abstract The Minimax Theorem is the most recognized theorem for determining strategies in a two person zerosum game. Other common strategies exist such
More informationDecision Analysis. Carlos A. Santos Silva June 5 th, 2009
Decision Analysis Carlos A. Santos Silva June 5 th, 2009 What is decision analysis? Often, there is more than one possible solution: Decision depends on the criteria Decision often must be made in uncertain
More informationINSE 6230 Total Quality Project Management
INSE 6230 Total Quality Project Management Lecture 6 Project Risk Management Project risk management is the art and science of identifying, analyzing, and responding to risk throughout the life of a project
More informationDecision Analysis REVISED TEACHING SUGGESTIONS ALTERNATIVE EXAMPLES
M03_REND6289_0_IM_C03.QXD 5/7/08 3:48 PM Page 7 3 C H A P T E R Decision Analysis TEACHING SUGGESTIONS Teaching Suggestion 3.: Using the Steps of the Decision-Making Process. The six steps used in decision
More information1. A is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes,
1. A is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. A) Decision tree B) Graphs
More informationDecision making in the presence of uncertainty
Lecture 19 Decision making in the presence of uncertainty Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square Decision-making in the presence of uncertainty Many real-world problems require to choose
More information56:171 Operations Research Midterm Examination Solutions PART ONE
56:171 Operations Research Midterm Examination Solutions Fall 1997 Answer both questions of Part One, and 4 (out of 5) problems from Part Two. Possible Part One: 1. True/False 15 2. Sensitivity analysis
More informationObjective of Decision Analysis. Determine an optimal decision under uncertain future events
Decision Analysis Objective of Decision Analysis Determine an optimal decision under uncertain future events Formulation of Decision Problem Clear statement of the problem Identify: The decision alternatives
More informationDr. Abdallah Abdallah Fall Term 2014
Quantitative Analysis Dr. Abdallah Abdallah Fall Term 2014 1 Decision analysis Fundamentals of decision theory models Ch. 3 2 Decision theory Decision theory is an analytic and systemic way to tackle problems
More informationDecision making in the presence of uncertainty
CS 2750 Foundations of AI Lecture 20 Decision making in the presence of uncertainty Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square Decision-making in the presence of uncertainty Computing the probability
More informationUNIT 10 DECISION MAKING PROCESS
UIT 0 DECISIO MKIG PROCESS Structure 0. Introduction Objectives 0. Decision Making Under Risk Expected Monetary Value (EMV) Criterion Expected Opportunity Loss (EOL) Criterion Expected Profit with Perfect
More informationReview of Expected Operations
Economic Risk and Decision Analysis for Oil and Gas Industry CE81.98 School of Engineering and Technology Asian Institute of Technology January Semester Presented by Dr. Thitisak Boonpramote Department
More informationDecision Theory. Course details. course notes 2008/2009. Studymanual (online) c L.C. van der Gaag, S. Renooij, P.
Decision Theory course notes 2008/2009 c L.C. van der Gaag, S. Renooij, P. de Waal Master Applied Computing Science, UU ICS Lecturer: Prerequisite: Literature: Examination: Course details dr. S. Renooij
More informationJohan Oscar Ong, ST, MT
Decision Analysis Johan Oscar Ong, ST, MT Analytical Decision Making Can Help Managers to: Gain deeper insight into the nature of business relationships Find better ways to assess values in such relationships;
More informationPhil 321: Week 2. Decisions under ignorance
Phil 321: Week 2 Decisions under ignorance Decisions under Ignorance 1) Decision under risk: The agent can assign probabilities (conditional or unconditional) to each state. 2) Decision under ignorance:
More informationAswath Damodaran 1 VALUATION: PACKET 3 REAL OPTIONS, ACQUISITION VALUATION AND VALUE ENHANCEMENT
1 VALUATION: PACKET 3 REAL OPTIONS, ACQUISITION VALUATION AND VALUE ENHANCEMENT Updated: January 2015 2 REAL OPTIONS: FACT AND FANTASY 3 Underlying Theme: Searching for an Elusive Premium TradiRonal discounted
More informationPERT 12 Quantitative Tools (1)
PERT 12 Quantitative Tools (1) Proses keputusan dalam operasi Fundamental Decisin Making, Tabel keputusan. Konsep Linear Programming Problem Formulasi Linear Programming Problem Penyelesaian Metode Grafis
More informationMaking Decisions Using Uncertain Forecasts. Environmental Modelling in Industry Study Group, Cambridge March 2017
Making Decisions Using Uncertain Forecasts Environment Agency Environmental Modelling in Industry Study Group, Cambridge March 2017 Green M., Kabir S., Peters, J., Georgieva, L., Zyskin, M., and Beckerleg,
More informationMaster of Business Administration - General. Cohort: MBAG/14/PT Mar. Examinations for Semester II / 2014 Semester I
Master of Business Administration - General Cohort: MBAG/14/PT Mar Examinations for 2013 2014 Semester II / 2014 Semester I MODULE: OPERATIONS RESEARCH MODULE CODE: MGMT5214 DURATION: 3 HOURS Instructions
More informationFDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.
FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.) Hints for Problem Set 2 1. Consider a zero-sum game, where
More informationEconomic Risk and Decision Analysis for Oil and Gas Industry CE School of Engineering and Technology Asian Institute of Technology
Economic Risk and Decision Analysis for Oil and Gas Industry CE81.98 School of Engineering and Technology Asian Institute of Technology January Semester Presented by Dr. Thitisak Boonpramote Department
More informationRisk Video #1. Video 1 Recap
Risk Video #1 Video 1 Recap 1 Risk Video #2 Video 2 Recap 2 Risk Video #3 Risk Risk Management Process Uncertain or chance events that planning can not overcome or control. Risk Management A proactive
More informationChapter 17 Student Lecture Notes 17-1
Chapter 17 Student Lecture Notes 17-1 Basic Business Statistics (9 th Edition) Chapter 17 Decision Making 2004 Prentice-Hall, Inc. Chap 17-1 Chapter Topics The Payoff Table and Decision Trees Opportunity
More informationEvent A Value. Value. Choice
Solutions.. No. t least, not if the decision tree and influence diagram each represent the same problem (identical details and definitions). Decision trees and influence diagrams are called isomorphic,
More informationOil prices and depletion path
Pierre-Noël GIRAUD (CERNA, Paris) Aline SUTTER Timothée DENIS (EDF R&D) timothee.denis@edf.fr Oil prices and depletion path Hubbert oil peak and Hotelling rent through a combined Simulation and Optimisation
More informationSequential-move games with Nature s moves.
Econ 221 Fall, 2018 Li, Hao UBC CHAPTER 3. GAMES WITH SEQUENTIAL MOVES Game trees. Sequential-move games with finite number of decision notes. Sequential-move games with Nature s moves. 1 Strategies in
More informationV. Lesser CS683 F2004
The value of information Lecture 15: Uncertainty - 6 Example 1: You consider buying a program to manage your finances that costs $100. There is a prior probability of 0.7 that the program is suitable in
More informationENGINEERING RISK ANALYSIS (M S & E 250 A)
ENGINEERING RISK ANALYSIS (M S & E 250 A) VOLUME 1 CLASS NOTES SECTION 2 ELEMENTS OF DECISION ANALYSIS M. ELISABETH PATÉ-CORNELL MANAGEMENT SCIENCE AND ENGINEERING STANFORD UNIVERSITY M. E. PATÉ-CORNELL
More informationMBF1413 Quantitative Methods
MBF1413 Quantitative Methods Prepared by Dr Khairul Anuar 5: Decision Analysis Part II www.notes638.wordpress.com Content 4. Risk Analysis and Sensitivity Analysis a. Risk Analysis b. b. Sensitivity Analysis
More informationChapter 2. An Introduction to Forwards and Options. Question 2.1
Chapter 2 An Introduction to Forwards and Options Question 2.1 The payoff diagram of the stock is just a graph of the stock price as a function of the stock price: In order to obtain the profit diagram
More informationHow to Consider Risk Demystifying Monte Carlo Risk Analysis
How to Consider Risk Demystifying Monte Carlo Risk Analysis James W. Richardson Regents Professor Senior Faculty Fellow Co-Director, Agricultural and Food Policy Center Department of Agricultural Economics
More informationSolutions for practice questions: Chapter 15, Probability Distributions If you find any errors, please let me know at
Solutions for practice questions: Chapter 15, Probability Distributions If you find any errors, please let me know at mailto:msfrisbie@pfrisbie.com. 1. Let X represent the savings of a resident; X ~ N(3000,
More informationMaking Hard Decision. ENCE 627 Decision Analysis for Engineering. Identify the decision situation and understand objectives. Identify alternatives
CHAPTER Duxbury Thomson Learning Making Hard Decision Third Edition RISK ATTITUDES A. J. Clark School of Engineering Department of Civil and Environmental Engineering 13 FALL 2003 By Dr. Ibrahim. Assakkaf
More informationComparison of Decision-making under Uncertainty Investment Strategies with the Money Market
IBIMA Publishing Journal of Financial Studies and Research http://www.ibimapublishing.com/journals/jfsr/jfsr.html Vol. 2011 (2011), Article ID 373376, 16 pages DOI: 10.5171/2011.373376 Comparison of Decision-making
More informationRepeated, Stochastic and Bayesian Games
Decision Making in Robots and Autonomous Agents Repeated, Stochastic and Bayesian Games Subramanian Ramamoorthy School of Informatics 26 February, 2013 Repeated Game 26/02/2013 2 Repeated Game - Strategies
More informationP1: PBU/OVY P2: PBU/OVY QC: PBU/OVY T1: PBU GTBL GTBL032-Black-v13 January 22, :43
CHAPTER19 Decision Analysis LEARNING OBJECTIVES This chapter describes how to use decision analysis to improve management decisions, thereby enabling you to: 1. Learn about decision making under certainty,
More information