Models & Decision with Financial Applications Unit 2: Structuring Decisions and Making Choices Duan LI Department of Systems Engineering & Engineering Management The Chinese University of Hong Kong http://www.se.cuhk.edu.hk/∼seem5820 2 Three fundamental steps in creating a decision model: 1. Identifying and structuring the values and objectives: • Identifying the issues that matter to the decision maker; • Separating the values into fundamental objectives and means objectives; • Specifying ways to measure accomplishment of the objectives. 2. Structuring the elements of the decision situations into a logical framework: Influence diagrams and decision trees; 3. Refinement and precise definition of all the elements of the decision model. • Clarity Test: Can we determine uniquely an outcome for each event? 3 Example: Hiring a summer intern for the Peach Tree Consumer Products: • Working under the supervision of a senior employee in the marketing group, the intern would focus primarily on the development of a market survey for certain products. • How to find an appropriate individual to fill this slot? • List all potential objectives for hiring summer intern 4 Table: Objective for hiring summer intern a) Maximize quality of market survey ←3 b) Sell more consumer products ←1 c) Build market share ←1 d) Identify new market niches for company’s products ←1 e) Minimize cost of survey design ←3 f) Try out prospective permanent employee ←4 g) Establish relationship with local college ←5 h) Provide assistance for senior employee ←2 i) Free up an employee to be trained for new assignment ←4 j) Learn updated techniques from intern-self, Supervisor, Market research department, Entire company ←4 k) Expose intern to real-world business experiences ←5 l) Maximize profit ←1 m) Improve company’s working environment by bringing in new and youthful energy ←2 n) Provide financial assistance for college student ←5 5 Classification 1) 2) 3) 4) 5) Business performance Improve the work environment Improve the quality and efficiency of marketing activities Personal and corporate development Community service Only items 2 to 5 are more in the decision context 6 Techniques for identifying objectives: 1. Develop a wish list. What do you want? What do you value? What should you want? 2. Identify alternatives. What is a perfect alternative, a terrible alternative, some reasonable alternative? What is good or bad about each? 3. Consider problems and shortcomings. What is wrong or right with your organization? What needs fixing? 4. Predict consequences. What has occurred that was good or bad? What might occur that you care about? 5. Identify goals, constraints and guidelines. What are your aspirations? What limitations are placed on you? 6. Consider different perspectives. What would your competitor or your constituency be concerned about? At some time in the future, what would concern you? 7 7. Determine strategic objectives. What are your ultimate objectives? What are your values that are absolutely fundamental? 8. Determine generic objectives. What objectives do you have for your customers, your employees, your shareholders, yourself? What environmental, social, economic, or health and safety objectives are important? 8 Separating the list of objectives into different kinds: • Separating means objectives (the objectives that help achieve other objectives) from fundamental objectives (the objectives that reflect what we really want to accomplish). • Fundamental objectives are organized into hierarchies. (Structuring the fundamental-objectives hierarchy is crucial for developing a multiple-objective decision model.) • Means objectives are organized into networks. 9 How to construct mean-objectives networks and fundamental-objectives hierarchies: To Move: Fundamental Objectives Downward in the Hierarchy: Means Objectives Away from Fundamental Objectives: Ask: To Move: “What do you mean by that?” Upward in the Hierarchy: “How could you achieve this?” Towards Fundamental Objectives: Ask: “Of what more general objective “Why is that important?” is this an aspect?” (WITI) When the fundamental objectives are specified, constructed and sorted out from the means objectives, we can turn to the process of structuring the various decision elements – decisions and alternatives, uncertain events and outcomes, and consequences. 10 Influence diagrams: • Rectangles represent decisions (decision node); • Ovals represent chance events (chance node); • A rectangle with round corners represents a mathematical calculation or a constant value (often the consequences) (consequence node or calculation node). • Nodes are put together in a graph, connected by arrows or arcs. • A node at the beginning of an arc is a predecessor and a node at the end of an arc is a successor. • An arc can represent either relevance or sequence • Properly constructed influence diagrams have no cycles. 11 Figure 1: 12 Figure 2: 13 Figure 3: 14 Decision Trees: • squares represent decisions (decision node); • The branches emanating from a square correspond to the choices available; • Circles represent chance events (chance node); • The branches emanating from a circle represent the possible outcomes of a chance event that are mutually exclusive and collectively exhaustive. 15 Decision tree analysis deals with logical analysis of choices among courses of action when 1. the consequence of an action will depend upon the “state of the world”, 2. the true state is as yet unknown, but 3. it is possible at a cost, by observing the outcome of an experiment, to obtain information about the true state. 16 Comparison of influence diagrams and decision trees: • Influence diagrams are excellent for displaying a decision’s basic structure, but they hide many of the details. • Decision trees display considerably more information than do influence diagrams. However, decision trees get “messy” much faster than do influence diagrams as decision problems become more complicated. • The ultimate decision made should not depend on the representation. 17 Solution methodology for decision trees: • Bellman’s Principle of Optimality: Any tail part of the optimal policy starting from a state in an intermediate stage must be also optimal with respect to that state. • Consider an application of dynamic programming to the shortest path problem. • Backwards induction – Averaging out and folding back for solving decision tree: – Compute the expected value at each chance node; – Select the best action at each decision node. • Decision tree analysis decomposes a sequential decision making problem into a family of single stage decision making problems. 18 Case Study – Texaco versus Pennzoil: In early 1984, Pennzoil and Getty Oil agreed to the terms of a merger. But before any formal documents could be signed, Texaco offered Getty a substantially better price, and Gordon Getty, who controlled most of the Getty stock, reneged on the Pennzoil deal and sold to Texaco.Pennzoil felt it had been dealt with unfairly and immediately filed a lawsuit against Texaco alleging that Texaco had interfered illegally in the Pennzoil-Getty negotiations. Pennzoil won the case, in late 1985, it was awarded $11.1 billion. A Texas appeals court reduced the judgment by $2 million, but interest and penalties drove the total back to $10.3 billion. James Kinnear, Texaco’s chief executive officer had promised to fight the case all the way to the US Supreme Court if necessary. In April 1987, just before Pennzoil began to file the liens, Texaco offered to pay Pennzoil $2 billion to settle the entire case. What should Hugh Liedtke, chairman of Pennzoil, do? 19 Risk Profiles: • The interpretation of EMV as the average amount that would be obtained by “realizing the uncertain event” a large number of times is not appropriate in many decision process. The EMV is NOT a perfect indicator of what might happen. • A risk profile is a graph that shows the chances associated with possible consequences. • Each risk profile is associated with a strategy, a particular immediate alternative, as well as specific alternatives in future decisions. • Risk profiles can be calculated for strategies that might not have appeared as optimal in an expected-value analysis. • By looking at the risk profiles, the decision maker can learn a lot about the riskiness of the alternatives. • A cumulative risk profile can be drawn from a risk profile. 20 Dominance: • A strategy is said to be dominated if, according to some rules relating to cumulative risk profiles, there exists a better strategy. • Strategy A is said to be of a deterministic dominance over strategy B, if strategy A (dominating strategy) pays off at least as much as Strategy B (dominated strategy). More specifically, strategy A deterministically dominates strategy B if there is a value x such that the chance of the payoff being less than or equal to x is 100% in alternative B, and the chance of the payoff being less than or equal to x is 0% in alternative A. • If two cumulative risk profiles are such that no part of the cumulative distribution function of Profile A lies to the left of the cumulative distribution function of Profile B, and at least some part of the cumulative distribution function of Profile A lies to the right of the cumulative distribution function of Profile B, then the strategy corresponding to Profile A stochastically dominates the strategy for Profile B. 21 • A dominated strategy can never be an optimal solution. • If one alternative dominates another, then the dominating alternative must have a higher expected value.