1 Chapter 3 Structuring Decisions Dr. Greg Parnell Department of Mathematical Sciences Virginia Commonwealth University

2 Overview Problem structuring Decision basis Structuring Objectives –Value Hierarchy –Means-Objectives Network Influence Diagram Decision Tree

3 Decision Analysis Is a Systematic Process Questions: Deliverables: What do we want? What do we know? What can we do? Values Value Hierarchy Information Alternatives Influence Diagram Decision Tree Value Model Sensitivity Analysis Critical Uncertainties What are the relationships? What is important? What are the possible outcomes? What are the probabilities of those outcomes? How much could we gain/lose? Probability Distributions Dominated Alternatives Risk Profiles Are we ready to decide OR how much more information would we be willing to pay for? Value of Information Value of Control Iteration Problem Structure Deterministic Analysis Probabilistic Analysis Evaluation Decision Initial Situation Problem Structuring

4 Decision Basis Values What do we want? Information What do we know? Alternatives What can we do? Problem structuring focuses on the values, alternatives, and information. We start with values. (We will use single value, usually NPV, until Chapter 15)

5 Structuring Objectives Identify objectives –Develop a wish list –Identify alternatives –Consider problems and shortcomings –Predict consequences –Identify, goals, constraints, and guidelines –Consider different perspectives –Determine strategic objectives –Determine generic objectives Sort or organize objectives into logical groups Keeney, R.L., (1994) "Creativity in Decision Making with Value-Focused Thinking," Sloan Management Review, Summer, First we identify, then we group the objectives.

6 Definitions fundamental objective(s): the decision-makers ultimate objective(s) objectives: the essential reasons for our interest in the decision situation objectives (value) hierarchy: a hierarchy that identifies what aspects of the higher level objective are important (Keeney/Clemen call this a fundamental-objectives hierarchy) means: specific approach to achieve our objectives means-objectives network: network whose purpose is to help generate alternatives by identifying the means to obtain our objectives

7 Example: Virginia Science Museum Experiencing queuing problems at the major exhibits –Why? Long lines, people leaving –What? Getting patrons into the museum –How? Cashiers with computer hardware and software –Who? Patrons, cashiers, managers –When? During the most popular exhibits –Where? Entrance to the museum

8 Objectives Hierarchy Science Museum of Virginia Fundamental Objective Objectives Subobjectives The objectives define the fundamental objective & subobjectives define the objectives.

9 Means-Objectives Network Provide incentives to arrive at non- peak times Improved software Improved hardware Cashier training Provide entertainment Separate processing for members Recruit members Add more means Connect the means to the subobjectives

10 Influence Diagrams - Node Types ID captures the DM’s state of information –Technique for decision structuring –Algorithms also exist to solve IDs –IDs have no cycles [IDs are not flow diagrams] Arrows are used for two purposes –Relevance: knowledge of the outcome of a predecessor node is useful to determine the outcome of a successor node –Sequence: the outcome of a predecessor node is known before the outcome of a successor node Chance Deterministic Value Decision

11 Venture Capitalist's Decision Questions: 1. What does the arc from Invest to Return on Investment mean? 2. What does the arc from Venture to Return on Investment mean? 3. Why is there no arc from Invest to Venture? 4. Why is there no arc from Venture to Invest? 5. How could the DM obtain additional information about the Venture?

12 Influence Diagram Modeling QUESTIONS 1. Describe how the two arrows model sequence and relevance? 2. What determines the number of possible consequences? 3. If we had three decision alternatives and four Market Activity outcomes, how many consequences would we have? This approach would be very cumbersome for large problems, fortunately, in many cases, we can use functions to simplify modeling.

13 Imperfect Information - Very Common QUESTIONS 1. Would you expect the Market Survey to be perfect or imperfect information? Why? 2. What is the effect of number of outcomes of the Market Survey have on the number of Payoff outcomes? Why? 3. Describe how the arrows model sequence and relevance? 4. Why do we draw the arrow from Actual Market to Market Survey versus the other direction? 5. What would an arrow from New Product to Actual Market mean?

14 Wildcat Oil ID Interpret this ID Some Common Influence Diagram Mistakes - IDs are not flow charts - NO CYCLES! Sequential decisions DPL Note: Read DPL Users Guide, pp Color of the arrows is the key!!!!

15 Probabilistic Modeling with IDs What is missing from this ID?

16 Decision Trees IDs are good for problem structuring since they suppress detail Decision trees - identify the sequence of decisions/events and have a branch for each decision alternative and each uncertain event outcome Decision tree must identify all paths Each outcome space must be ME & CE ! Develop the decision tree for each of the IDs we have developed

17 New Product Decision How many outcomes (at the end of the DT) are there? How many Payoffs need to be calculated?

18 Decision Tree How many outcomes (at the end of the DT) are there? How many Payoffs need to be calculated?

19 Probability Tree What node type is missing? How many outcomes (at the end of the DT) are there? How many Payoffs need to be calculated?

20 Decision Trees Versus Influence Diagrams Influence diagrams Good for problem structuring Good for communicating with management - suppress details Decision trees Show details - better for asymmetric problems Complementary - DPL uses both representations

21 Clarity Test Elements of a decision must be clearly defined DM, DM's staff, decision analyst Clairvoyant = access to all future information Clarity Test (Howard, 1988) Your model passes the clarity test if a clairvoyant would be able to unequivocally tell you the outcome of any event in the ID/decision tree EXAMPLE: Does the following uncertain variable pass the clarity test?

22 Summary Problem structuring Decision basis Structuring objectives –Value hierarchy –Means-objectives network Influence diagram –Types of nodes Decision tree –Types of nodes Comparison –Advantages of each problem structuring method Clarity test