Chapter 17 Decision Making 17.1 Payoff Table and Decision Tree 17.2 Criteria for Decision Making

Introduction Single criteria decisions (e.g. I want the fastest car) are easier to make than multiple criteria decisions (e.g. I want the best car). Decision making: should I take a particular course of action?

Four basic features: Alternative Courses of Action. –Without options there is not much to do. Events or States of the World. –What can happen and what is the likelihood. Payoffs. –Value of each event must be known. Decision Criteria.

17.1: Payoff Tables and Decision Trees Payoff Table (PT) contains the events that could happen for each course of action. PT also contains the payoff. PT might contain the probabilities of events.

Decision Tree Decision Tree (DT) shows the events and courses of action. DT also shows the payoffs. DT also shows the probabilities of events. The DT is constructed of branches and nodes. There can be any number of branches.

Criteria and Probabilities Even without the probabilities and payoffs, DTs are useful for communicating or inspiring thought. With the payoffs, probabilities and a decision making criterion, you can evaluate the courses of action. Payoffs: both Profit and Opportunity Loss (OL) can be found. OL is the profit lost by failing to choose the best course of action. OL = best profit for current event – profit being considered (current action and event). OL ≥ 0.

17.2: Criteria for Decision Making Probabilities of events will be needed to calculate expected outcomes. Where do the probabilities come from? Four criteria: –Expected Monetary Value –Expected Opportunity Loss –Expected Value of Perfect Information –Return-to-risk Ratio

Expected Monetary Value The Expected Monetary Value or EMV is often used as a decision making criterion. EMV = sum of the product of profit and probability for all combinations of events and actions. Typically choose the largest EMV.

Expected Opportunity Loss Expected Opportunity Loss (EOL) is the sum of the product of the probability and opportunity loss for each event under each decision. Formula 17.2.

Expected Value of Perfect Information If you find the expected opportunity loss (EOL) for the “best” decision, you will have the expected value of perfect information (EVPI). EVPI = expected profit under certainty – EMV of the best alternative. Expected profit under certainty = the sum of the product of probability and best profit for all outcomes or states.

Return-to-Risk Ratio (RTRR) EMV and EOL do not consider variability. Use the definition of standard deviation for a random variable to approximate the risk (chapter 5!). Calculate the Return-to-Risk ratio for each course of action = EMV divided by standard deviation. See formula Return-to-Risk is the reciprocal of the coefficient of variation.