Homework due next Tuesday, September 22 p. 156 # 5-7, 5-8, 5-9 Please use complete sentences to answer any questions and make. Include any tables you are asked to make.

Chapter 5: Decision-making Concepts Quantitative Decision Making with Spreadsheet Applications 7 th ed. By Lapin and Whisler Section 5-7: Decision Tree Analysis Some slides are from Business Statistics: A Decision-Making Approach 6 th Edition found at

The Bayes Decision Rule Takes into account all the information about the chances for various payoffs. Takes into account all the information about the chances for various payoffs. Event (level of demand ) Probability Act (Choice of Movement) Gears & Levers Spring Action Weights & Pulleys Payoff Payoff x Prob Payoff Payoff Light.10 $ 25,000 $ $10,000 -$ $125,000 - $12,500 Moderat e , , , ,000400, ,00 0 Heavy , , , ,000750, ,00 0 ExpectedPayoff:$412,500$455,000$417,500

Other Decision Criteria Maximin Payoff Criterion – choose the best of the worst outcomes. Maximin Payoff Criterion – choose the best of the worst outcomes. Maximum Likelihood Criterion – focus on the most likely event to the exclusion of all others. Maximum Likelihood Criterion – focus on the most likely event to the exclusion of all others. The Criterion of Insufficient Reason – every event has the same probability. The Criterion of Insufficient Reason – every event has the same probability.

Table vs. Tree Payoff table: simple decisions Payoff table: simple decisions Decisions made at different points in time with uncertain events occurring between decisions. Decisions made at different points in time with uncertain events occurring between decisions. Tree gives more flexibility. Tree gives more flexibility. Tree shows every possible course of action and all possible outcomes. Tree shows every possible course of action and all possible outcomes.

Decision Tree A decision tree is a picture of all the possible courses of action and the consequent possible outcomes. A box is used to indicate the point at which a decision must be made, A box is used to indicate the point at which a decision must be made, The branches going out from the box indicate the alternatives under consideration The branches going out from the box indicate the alternatives under consideration A circle represents an event (usually has a probability) A circle represents an event (usually has a probability) The branches going out from the circle represent outcomes of the event. The branches going out from the circle represent outcomes of the event.

Sample Decision Tree Large factory Small factory Average factory Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy

Add Probabilities and Payoffs Large factory Small factory Decision Average factory Uncertain Events (States of Nature) Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy (continued) PayoffsProbabilities (.3) (.5) (.2) (.3) (.5) (.2) (.3) (.5) (.2)

Decision Tree Analysis  Each node is evaluated in terms of its expected payoff.  Event forks: expected payoffs are computed.  Act forks: the greatest value is brought back.  The decision tree is folded back by maximizing expected payoff.  Inferior acts are pruned from the tree.  The pruned tree indicates the best course of action, the one maximizing expected payoff.  The process works backward in time.

Fold Back the Tree Large factory Small factory Average factory Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy (.3) (.5) (.2) (.3) (.5) (.2) (.3) (.2) EV=200(.3)+50(.5)+(-120)(.2)= 61 EV=90(.3)+120(.5)+(-30)(.2)= 81 EV=40(.3)+30(.5)+20(.2)= 31 (.5)

Make the Decision Large factory Small factory Average factory Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy Strong Economy Stable Economy Weak Economy (.3) (.5) (.2) (.3) (.5) (.2) (.3) (.5) (.2) EV= 61 EV=81 EV= 31 Maximum EV=81