CHAPTER 19 Decision Theory to accompany Introduction to business statistics fourth edition by ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. stengel o 2002 The Wadsworth Group
CHAPTER 19: Decision Theory to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group
l Chapter 19-Learning objectives Express a decision situation in terms of decision alternatives, states of nature, and payoffs Differentiate between non-Bayesian and Bayesian ecision criteria Determine the expected payoff for a decision alternative Calculate and interpret the expected value of perfect information Express and analyze the decision situation in terms of opportunity loss and expected opportunity loss Apply incremental analysis to inventory-level decisions o 2002 The Wadsworth Group
Chapter 19 - Learning Objectives • Express a decision situation in terms of decision alternatives, states of nature, and payoffs. • Differentiate between non-Bayesian and Bayesian decision criteria. • Determine the expected payoff for a decision alternative. • Calculate and interpret the expected value of perfect information. • Express and analyze the decision situation in terms of opportunity loss and expected opportunity loss. • Apply incremental analysis to inventory-level decisions. © 2002 The Wadsworth Group
l Chapter 19- Key Terms Levels of doubt Maximin criteria Risk Maximax criteria Uncertainty Minimax regret gnorance Expected value of · Decision situation perfect information Decision alternatives States of nature Expected opportunity Probabilities Incremental analysis Expected payoff o 2002 The Wadsworth Group
Chapter 19 - Key Terms • Levels of doubt – Risk – Uncertainty – Ignorance • Decision situation – Decision alternatives – States of nature – Probabilities – Expected payoff • Maximin criteria • Maximax criteria • Minimax regret • Expected value of perfect information • Expected opportunity loss • Incremental analysis © 2002 The Wadsworth Group
l The Decision situation The decision maker can control which decision alternative(row)is selected but cannot determine which state of nature (column will occur The decision alternative is selected prior to knowing the state of nature o 2002 The Wadsworth Group
The Decision Situation • The decision maker can control which decision alternative (row) is selected but cannot determine which state of nature (column) will occur. • The decision alternative is selected prior to knowing the state of nature. © 2002 The Wadsworth Group
I An example Problem 19.34: a ski resort operator must decide before the winter season whether he will lease a snow making machine. If he has no machine, he will make $20,000 if the winter is mild, $30,000 if it is typical, and $50,000 if the winter is severe. If he decides to lease the machine, his profits for these conditions will be $30,000, $35,000, and $40,000, respectively. The probability of a mild winter is 0.3, with a 0.5 chance of a typical winter and a 0.2 chance of a severe winter. If the operater wants to maximize his expected profit should he lease the machine? what is the most he should be willing to pay for a perfect forecast? o 2002 The Wadsworth Group
An Example • Problem 19.34: A ski resort operator must decide before the winter season whether he will lease a snowmaking machine. If he has no machine, he will make $20,000 if the winter is mild, $30,000 if it is typical, and $50,000 if the winter is severe. If he decides to lease the machine, his profits for these conditions will be $30,000, $35,000, and $40,000, respectively. The probability of a mild winter is 0.3, with a 0.5 chance of a typical winter and a 0.2 chance of a severe winter. If the operater wants to maximize his expected profit, should he lease the machine? What is the most he should be willing to pay for a perfect forecast? © 2002 The Wadsworth Group
lI The Decision Situation: An E: xample The decision alternatives are The operator does not lease the snow-making machine The operator does lease the snow-making machine The states of nature are The winter is mild The winter is typical The winter is severe o 2002 The Wadsworth Group
The Decision Situation: An Example • The decision alternatives are: – The operator does not lease the snow-making machine. – The operator does lease the snow-making machine. • The states of nature are: – The winter is mild. – The winter is typical. – The winter is severe. © 2002 The Wadsworth Group
Ⅷ The Payoff Table State State 2 State 3 (P=p)(P=p2)(P=p3) Decision 12 13 Alternative 1 Decision 21 Alternative 2 Decision 32 33 alternative 3 where vi is the payoff value associated with the selecting Alternative i and having State j occur, and pi is the probability that State occurs o 2002 The Wadsworth Group
The Payoff Table where vij is the payoff value associated with the selecting Alternative i and having State j occur, and pj is the probability that State j occurs. State 1 (P = p1 ) State 2 (P = p2 ) State 3 (P = p3 ) Decision Alternative 1 v11 v12 v13 Decision Alternative 2 v21 v22 v23 Decision Alternative 3 v31 v32 v33 © 2002 The Wadsworth Group
ll The Payoff Table: An example States of nature Winter Winter Winter Decision Mild Typical| Severe Alternatives(0.3)(0.5)(0.2 Does not lease snow-making 20,000$30000$50,000 machine Does lease snow-making/$30,000$35,000$40,00 machine o 2002 The Wadsworth Group
The Payoff Table: An Example States of Nature D ecision A lternatives Winter Mild (0.3) Winter Typical (0.5) Winter Severe (0.2) Does not lease snow-making machine $20,000 $30,000 $50,000 Does lease snow-making machine $30,000 $35,000 $40,000 © 2002 The Wadsworth Group
l The Decision Tree Decision Alternatives State of nature payoff Pi State 1 Occurs 11 Select Alternative/p2 State 2 Occurs 12 p3 State 3 Occurs pi State 1 Occurs Select Alternative 2/p2 State 2 Occurs v2 pa State 3 Occurs_ v23 pi State 1 Occurs Select alternative 3 p, State 2 Occurs v32 、p3 State3 Occurs y3 o 2002 The Wadsworth Group
The Decision Tree p1 State 1 Occurs v11 p2 State 2 Occurs v12 p3 State 3 Occurs v13 p1 State 1 Occurs v21 p2 State 2 Occurs v22 p3 State 3 Occurs v23 p1 State 1 Occurs v31 p2 State 2 Occurs v32 p3 State 3 Occurs v33 Select Alternative 1 Select Alternative 2 Select Alternative 3 Decision Alternatives State of Nature Payoff © 2002 The Wadsworth Group
ll The Decision Tree: An example Does not lease snow- 0. 3 Winter mild 20000 making machine 0.5 Winter typical $30,000 0.2 Winter severe $50,000 Does lease snow- 0.3 Winter mild $30,000 making machine 0.5 Winter typical $35,000 0.2 Winter severe $40, 000 o 2002 The Wadsworth Group
The Decision Tree: An Example 0.3 Winter mild $20,000 0.5 Winter typical $30,000 0.2 Winter severe $50,000 0.3 Winter mild $30,000 0.5 Winter typical $35,000 0.2 Winter severe $40,000 Does not lease snowmaking machine Does lease snowmaking machine © 2002 The Wadsworth Group
