# © 2008 Prentice-Hall, Inc. Decision Analysis. © 2009 Prentice-Hall, Inc. 3 – 2 Decision Trees decision tree Any problem that can be presented in a decision.

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© 2008 Prentice-Hall, Inc. Decision Analysis

© 2009 Prentice-Hall, Inc. 3 – 2 Decision Trees decision tree Any problem that can be presented in a decision table can also be graphically represented in a decision tree Decision trees are most beneficial when a sequence of decisions must be made decision points nodesstate-of-nature points nodes All decision trees contain decision points or nodes and state-of-nature points or nodes A decision node from which one of several alternatives may be chosen A state-of-nature node out of which one state of nature will occur

© 2009 Prentice-Hall, Inc. 3 – 3 Five Steps to Decision Tree Analysis 1.Define the problem 2.Structure or draw the decision tree 3.Assign probabilities to the states of nature 4.Estimate payoffs for each possible combination of alternatives and states of nature 5.Solve the problem by computing expected monetary values ( EMV s) for each state of nature node

© 2009 Prentice-Hall, Inc. 3 – 4 Structure of Decision Trees Trees start from left to right Represent decisions and outcomes in sequential order Squares represent decision nodes Circles represent states of nature nodes Lines or branches connect the decisions nodes and the states of nature

© 2008 Prentice-Hall, Inc. Each chance node must have branches that correspond to a set of mutually exclusive and collectively exhaustive outcomes. Two outcomes are mutually exclusive (or disjoint) if the occurrence of one of the outcomes precludes the simultaneous occurrence of the other. If you make a list of the outcomes which can occur when you adopt a particular course of action then this list is said to be exhaustive if your list includes every possible outcome.

© 2009 Prentice-Hall, Inc. 3 – 6 Double-Risk Dilemma Assume that you have a ticket that will let you participate in a game of chance (a lottery) that will pay off \$10 with a 45% chance (or a 55% chance of nothing). Your friend has a ticket to a different lottery that has a 20% chance of paying \$25 (or an 80% chance of nothing). Your friend has offered to let you have his ticket if you will give him your ticket plus \$1. Should you agree to the trade and play to win \$25, or should you keep your ticket?

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© 2009 Prentice-Hall, Inc. 3 – 8 Thompson Lumber Company STATE OF NATURE ALTERNATIVE FAVORABLE MARKET (\$) UNFAVORABLE MARKET (\$) Construct a large plant200,000–180,000 Construct a small plant100,000–20,000 Do nothing00 Table 3.1

© 2009 Prentice-Hall, Inc. 3 – 9 Thompson s Decision Tree Favorable Market Unfavorable Market Favorable Market Unfavorable Market Do Nothing Construct Large Plant 1 Construct Small Plant 2 A Decision Node A State-of-Nature Node

© 2009 Prentice-Hall, Inc. 3 – 10 Thompson s Decision Tree Favorable Market Unfavorable Market Favorable Market Unfavorable Market Do Nothing Construct Large Plant 1 Construct Small Plant 2 Alternative with best EMV is selected EMV for Node 1 = \$10,000 = (0.5)(\$200,000) + (0.5)(–\$180,000) EMV for Node 2 = \$40,000 = (0.5)(\$100,000) + (0.5)(–\$20,000) Payoffs \$200,000 –\$180,000 \$100,000 –\$20,000 \$0 (0.5)

© 2009 Prentice-Hall, Inc. 3 – 11 Texaco vs. 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 Oil a substantially better price. Getty Oil agreed and sold to Texaco. In 1985, Pennzoil filed a lawsuit against Texaco. And won the case…awarded \$11.0 billion. Texaco appealed ----- court \$10.3 billion. Texaco threat to file for bankruptcy if Pennzoil secured the judgment.

© 2009 Prentice-Hall, Inc. 3 – 12 In 1987, Texaco offered to pay Pennzoil \$2billion to settle the case. Pennzoil chairman indicated that a settlement between \$2 and \$5 billion would be fair. Should Pennzoil accepts or refuses and make a counteroffer of \$5billion? Texaco Might 1- Accepts to pay \$5 billion 2- Refuses and counteroffer of \$3 billion 3- Refuses and goes to court

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© 2009 Prentice-Hall, Inc. 3 – 15 EMV = 4.56

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© 2009 Prentice-Hall, Inc. 3 – 17 EMV = 4.56

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© 2009 Prentice-Hall, Inc. 3 – 20 Decision Path: A path starting at the left most node up to the values at the end of a branch by selecting one alternative from a decision node or by following one outcome from uncertainty nodes. Decision Strategy: The collection of decision paths connected to a branch of the left most node by selecting one alternative from each decision node along these paths. Optimal Decision Strategy: That Decision Strategy which results in the highest EMV if we maximize profit and the lowest EMV if we minimize cost.

© 2009 Prentice-Hall, Inc. 3 – 21

© 2009 Prentice-Hall, Inc. 3 – 22 D1 =Accept 2 Billion

© 2009 Prentice-Hall, Inc. 3 – 23 D2 = Counter 5 Billion, Refuse Counter of \$3 Billion

© 2009 Prentice-Hall, Inc. 3 – 24 D3 = Counter 5 Billion, Accept \$3 Billion

© 2009 Prentice-Hall, Inc. 3 – 25 OPTIMAL DECISION STRATEGY Counteroffer \$5 Billion. Next, if Texaco Counteroffers \$3 Billion, refuse the counteroffer. Number of Decision Strategies in Decision Tree above: 3

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