Structuring Decisions Dr. Yan Liu Department of Biomedical, Industrial & Human Factors Engineering Wright State University
Introduction • Step 1: Identifying and Structuring the Values and Objectives • Identifying issues that matter • Listing objectives and separating means and fundamental objectives • Specifying measures of fundamental objectives • Step 2: Structuring the Elements of Decision Situation into a Logical Framework • Structuring logic and time sequence among decisions, uncertain events, and consequences • Tools: influence diagrams and decision trees • Step 3: Refining and Precisely Defining the elements • The decisions to be made and the available alternatives • Probability distributions of uncertain events through a combination of data analysis and expert judgment • Measures of consequences and tradeoffs
Identifying and Structuring Values and Objectives • Listing the Objectives (Table 3.2 at page 45) • Develop a wish list (What do/should we want and value?) • Determine strategic objectives (What are our ultimate goals?) • Determine generic objectives (what are our objectives for customers, our family, or ourselves?) • Identify alternatives (what are perfect/terrible/reasonable alternatives and their good/bad sides?) • Consider problems and shortcomings (what is wrong/right? what needs fixing?) • Predict consequences (what might occur to what we care about?) • Identify goals, constraints, and guidelines (what are our aspirations and limitations placed on you?) • Consider different perspectives (what would be our competitor’s concern?)
Identifying and Structuring Values and Objectives (Cont.) • Categorizing Objectives • Sort the list of objectives and group them into categories • Removing Irrelevant Objectives • Separating Means and Fundamental Objectives • Means objectives are those helping to achieve other objectives • e.g. One objective of taking this class is to maximize your learning of decision analysis process • Fundamental objectives are those reflecting what we want to accomplish ultimately • e.g. One objective of going for a vacation is to maximize relaxation • Whether an objective is a means or fundamental objective can be a subjective judgment
Identifying and Structuring Values and Objectives (Cont.) • Fundamental Objectives Hierarchy • Upper levels represent more general objectives • Lower levels describe important elements of the more general levels • Lowest-level fundamental objectives are the basis on which consequences are measured A Fundamental Hierarchy of Vehicle Regulation
Identifying and Structuring Values and Objectives (Cont.) • Means Objectives Networks • A means objective can be connected to several other objectives to indicate it helps achieve them A Means Objective Network of Vehicle Regulation
Identifying and Structuring Values and Objectives (Cont.) Techniques for Organizing Objectives
Summer Intern Example The Peach Tree Consumer Products Inc. has an opening for a summer intern. 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 of the company’s products. The problem is how to find an appropriate individual to fill this slot.
Maximize quality of market survey; • Sell more consumer products; • Build market share; • Identify new market niches for company’s products; • Minimize cost of survey design; • Try out prospective permanent employee; • Establish relationship with local college; • Provide assistant to senior employee; • Free up an employee to be trained for new assignment; • Learn updated techniques from intern; • Expose intern to real-world business experience; • Maximize profit; • Provide financial assistance to college students List of Objectives
Categorized Objectives: • Boost Business Performance • Sell more products, maximize profit, increase market share, identify market niche • Improve Work Environment • Bring in new energy, assist senior employee • Improve the quality and efficiency of marketing activities • Maximize survey quality, minimize survey cost • Better Personnel and Corporate Development • Lean updated techniques, free up employees for new assignment, try out prospective employee • Increase the Engagement of Community Service • Financial aid, expose intern to real world, relationship with local colleges
Structuring Decision Problems • Step 1: Identifying and Structuring the Values and Objectives • Step 2: Structuring the Elements of Decision Situation into a Logical Framework • Step 3: Refine and Precisely Define the Elements
Chance Node Decision Node Venture Succeeds or Fails Invest? Return on Investment Computer Industry Growth Computation Node Overall Satisfaction Payoff Node Influence Diagrams Influence Diagram of a Venture Capitalist’s Decision Problem
Influence Diagrams (Cont.) Relationships between nodes are symbolized with arrows or directed arcs Distinctions are made here between sequence and dependence arcs only for teaching purposes. Once you are familiar with the differences, you can use solid arcs throughout the influence diagram like the convention used in the textbook
Influence Diagrams (Cont.) • Influence Diagrams and Fundamental Objectives Hierarchy • The Payoff node corresponds to the most general objective (located at the upper-most level) in the fundamental-objectives hierarchy • The computation nodes correspond to the objectives at the lower levels in the hierarchy
Basic Influence Diagrams • Basic Risky Decision • Whether the potential gain in the risky choice is worth the risk Investment Example You have $2,000 to invest and the objective is to earn as high a return on your investment as possible. There are two alternatives: investing in a friend’s business or keeping the money in a savings account with a fixed interests rate. If you invest in the business, your return depends on the success of the business. You figure there could be two possible outcomes: the business is either widely successful earning you $3,000 beyond your initial investment (hence leaving you $5,000 in total) or a total flop, in which case you will lose all your money. On the other hand, if you put your money into a saving account, you will earn $200 in interest regardless of your friend’s business.
Basic Influence Diagrams (Cont.) • Imperfect Information • Imperfect information about some uncertain event (e.g. forecast and estimate) will affect the eventual payoff Evacuation Example Suppose you live in Miami. A hurricane near the Bahama Islands threatens to cause severe damage. As a result, the authorities recommend everyone to evacuate. Although the evacuation is costly, you would be safe. On the other hand, staying is risky. You could be injured or even killed if the storm comes ashore within 10 miles of your home. If the hurricane’s path changes, however, you would be safe without having incurred the cost of evacuating. The two fundamental objectives are to maximize your safety and to minimize your costs. Undoubtedly, you will pay close attention to the weather forecasters who would predict the course of the storm. However, the weather forecasters are not perfect predictors because not everything is known about hurricanes.
Hurricane Path Forecast Decision Consequence dependence sequence Influence Diagram of the Evacuation Decision Problem
Basic Influence Diagrams (Cont.) • Sequential Decisions • Two or more decisions that need to be made in sequence Evacuation Example Suppose in the example of hurricane-evacuation decision, you are waiting anxiously for the forecast as the hurricane is bearing down. Should you keep waiting for the forecast or leave immediately? In this case, you are facing a sequential decision situation. If you decide to wait for the forecast, then your next decision is whether you should evacuate or stay based on the forecast information.
Hurricane Path Forecast Evacuate? Consequence sequence Wait for Forecast? Influence Diagram of the Sequential Evacuation Decision Problem
Cost Revenue Introduce Product? Profit Basic Influence Diagrams (Cont.) • Computation Nodes (Intermediate Calculations ) • Emphasizing the structure of the influence diagram, especially when a node receives inputs from many other nodes • Used in the same way as payoff nodes • Their values can be calculated directly from inputs of predecessor nodes Product Example Suppose a firm is considering introducing a product, and its fundamental objective is to maximize the profit. 1st Version
Fixed Cost Fixed Cost Units Sold Units Sold Unit Variable Cost Variable Cost Price/unit? Introduce Product? Price/unit? Introduce Product? Profit Profit Revenue Cost Basic Influence Diagrams 2nd Version 3rd Version
Constructing an Influence Diagram • No set strategy is given; a good approach is to put together a simple version of the diagram first and then add details as necessary • Steps for Constructing Influence Diagram • 1. Identify the decisions to be made. If there are more than one decision, determine their time sequence and draw sequence arcs to connect the decision nodes • 2. Structure fundamental objectives hierarchy and convert the fundamental objectives into payoff or computation nodes in the influence diagram • 3. Identify relevance relationships between the decision nodes and computation nodes or payoff node and draw corresponding arcs • 4. Identify all the uncertain events • 5. Identify the sequence relationships between the chance nodes and decision nodes and draw corresponding arcs • 6. Identify the relevance relationships between the chance nodes and draw corresponding arcs
Constructing an Influence Diagram • Steps for Constructing Influence Diagram (Cont.) • 7. Identify the relevance relationships between the chance nodes and computation nodes or payoff node and draw corresponding arcs • 8. Check the appropriateness of the influence diagram (any missing and/or irrelevant information)
EPA Example The Environmental Protection Agency (EPA) often must decide whether to permit the useof an economically beneficial chemical that may induce cancer (carcinogenic). Furthermore, the decision often must be made without perfect informationabout either the long-term benefitsor health hazards. Alternative courses of actions are to permit the use of the chemical, restrict its use, or to ban it all together. Tests can be runto learn something about the carcinogenic potential, and survey datacan give an indication of the extent to which people are exposed when they do use the chemical. These pieces of information are both important in making the decision. For example, if the chemical is only mildly toxic and the exposure rate is minimal, then restricted use may be reasonable. On the other hand, if the chemical is only mildly toxic but the exposure rate is high, then banning its use may be imperative.
Survey Lab Test Exposure Rate Net Value Carcinogenic Potential Economic Value Cancer Cost Usage Decision? Influence Diagram of the EPA Decision Problem Net Value Cancer Cost Economic Value
Survey Lab Test Cancer Risk Exposure Rate Net Value Carcinogenic Potential Economic Value Cancer Cost Usage Decision? Influence Diagram of the EPA Decision Problem (adding a computation node)
Comments on Influence Diagrams • NOT a flowchart of the decision process • A snapshot of the decision situation at a particular time • Sequencing is implied • Should NEVER contain cycles (no feedbacks) • Very compact notations that hide lots of information • Interpreting an influence diagram is generally easy • Good for conveying model design to others • Creating influence diagrams can be difficult
Decision Trees • Decision Trees Display A Decision Problem in Detail • Decision trees explicitly identify the sequence of decisions/events (from left to right) • Decision trees show all possible future scenarios • One branch for each decision alternative • One branch for each outcome of an uncertain event (outcomes must be mutually exclusive and collectively exhaustive)
Decision Trees (Cont.) Decision Alternative Chance Node Consequence Widely Success $3,000 Business Decision Node Flop $0 Business Result Outcome of Uncertain Event Investment Choice $200 Savings Decision Tree of the Investment Decision Problem
Basic Decision Trees • Basic Risky Decision Politician Example The fundamental objective of a politician is to have a career that provides leadership for the country and representation for her constituency. She can do so to a varying degrees by serving in Congress. She might have two options: 1) running for reelection to her U.S. House of Representatives seat, in which case her reelection is virtually assured; and 2) running for a Senate seat, in which case there is a chance of losing. If she loses, she could return to her old job as a lawyer (the worst possible outcome). The best possible outcome is to win the Senate place in terms of her objective of providing leadership and representation.
Running Decision Election Result Decision Tree of the Politician’s Basic Risk Decision
Basic Decision Trees • Double-Risk Decision Dilemma • Decide between two risky prospects Election Result Running Decision Election Result The Politician’s Double- Risk Decision Dilemma
Court Result Basic Decision Trees • Range-of-Risk Decision Dilemma • The outcomes of the chance events are a range of values Insurance Example An individual has sued for damages of $450,000 because of injury. The insurance company has offered to settle for $100,000. The plaintiff must decide whether to accept the settlement or go to court. Decision Tree of the Insurance Example
Basic Decision Trees • Imperfect Information • Placing the corresponding chance node prior to the decision that it affects Evacuation Decision Forecast Evacuation Decision Decision Tree of the Evacuation Decision Problem
Basic Decision Trees • Sequential Decisions • Order decisions in decision trees from left to right Wait Decision Evacuation Decision Evacuation Decision Decision Tree of the Sequential Evacuation Decision Problem
Basic Decision Trees • Schematic Representation of Sequential Decisions • In problems with many decisions involved, the sizes of full-blown decision trees can increase exponentially
Compare Influence Diagrams and Decision Trees • Both influence diagrams and decision trees have strength and weakness and can complement each other
Structuring Decision Problems • Identifying and Structuring the Values and Objectives • Step 2: Structuring the Elements of Decision Situation into a Logical Framework • Step 3: Refine and Precisely Define the Elements
Decision Details • Define Elements of the Decision Clearly • e.g. In the Environmental Protection Agency example, one fundamental objective is to minimize the social cost of cancer. How will the cancer cost be measured, in terms of incremental lives cost or incremental cases of cancer? Include both treatable and fatal? One uncertain event is rate of exposure. What are the possible outcomes? How to measure? The number of people exposed to the chemical per day or per hour? • Every Element of the Decision Model Needs to Pass the Clarity Test • Various people involved in the decision think about the decision elements in exactly the same way; no misunderstandings regarding the definitions of the basic decision elements • Cash Flows and Probabilities • Specific chances associated with each outcome of uncertain events • Specific cash flows at different times
Research-and-Development Example A company needs to decide whether to spend $2M to continue with a particular research project. The success of the project (measured by obtaining a patent) is not assured. At this point, the decision maker judges only a 70% chance of getting the patent. If the patent is awarded, the company can either license the patent for an estimated $25M or invest an additional $10M to create a production and marketing system to sell the product directly. If the company chooses the latter, it faces uncertainty of demand and associated profit from sales.
License Technology $23M Demands High Patent Awarded $25M Continue Development $43M (p=0.25) $55M (p=0.7) Develop Production and Marketing to Sell Product Production Decision -$2M Med. $21M Development Result (p=0.55) $33M Market Result -$10M Low $3M (p=0.20) $15M No Patent Development Decision -$2M (p=0.3) Stop Development $0 A Decision Tree Representation (With Cash Flows and Probabilities Specified) of the Research-and-Development Decision Problem
Decision Details • Defining Measurement Scales for Fundamental Objectives • Objectives with natural attribute scales can be measured objectively • e.g. monetary values, time, length, weight, etc. • Objectives without natural attribute scales • e.g. public image, quality of life, etc. • Measured indirectly with proxies • e.g. GPA as a measure of a person’s intelligence • Measured subjectively using an attribute rating scale • e.g. The quality of life can be measured using a five-point Likert scale questionnaire (best, better, satisfactory, worse, and worst)