Chapter 17 Student Lecture Notes 17-1
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1 Chapter 17 Student Lecture Notes 17-1 Basic Business Statistics (9 th Edition) Chapter 17 Decision Making 2004 Prentice-Hall, Inc. Chap 17-1 Chapter Topics The Payoff Table and Decision Trees Opportunity loss Criteria for Decision Making Expected monetary value Expected opportunity loss Return-to-risk ratio Expected Profit Under Certainty Decision Making with Sample Information Utility 2004 Prentice-Hall, Inc. Chap 17-2 Features of Decision Making List Alternative Courses of Action List Possible Events or Outcomes or States of Nature Determine Payoffs Associate a payoff with each course of action and each event pair Adopt Decision Criteria Evaluate criteria for selecting the best course of action 2004 Prentice-Hall, Inc. Chap 17-3
2 Chapter 17 Student Lecture Notes 17-2 List Possible Actions or Events Two Methods of Listing Payoff Table Decision Tree 2004 Prentice-Hall, Inc. Chap 17-4 Payoff Table (Step 1) Consider a food vendor determining whether to sell soft drinks or hot dogs. Course of Action (A j ) Event (E i ) Sell (A 1 ) Sell (A 2 ) Cool Weather (E 1 ) x 11 =$50 x 12 = $100 Warm Weather (E 2 ) x 21 = $200 x 22 = $125 x ij = payoff (profit) for event i and action j 2004 Prentice-Hall, Inc. Chap 17-5 Payoff Table (Step 2) Do Some Actions Dominate? Action A dominates action B if the payoff of action A is at least as high as that of action B under any event and is higher under at least one event Action A is inadmissible if it is dominated by any other action(s) Inadmissible actions do not need to be considered Non-dominated actions are called admissible 2004 Prentice-Hall, Inc. Chap 17-6
3 Chapter 17 Student Lecture Notes 17-3 Payoff Table (Step 2) Do Some Actions Dominate? (continued) Event (E i ) Level of Demand Low Moderate High Course of Action (A j ) Production Process A B C D Action C dominates Action D Action D is inadmissible 2004 Prentice-Hall, Inc. Chap 17-7 Decision Tree: Example Food Vendor Profit Tree Diagram Cool Weather Warm Weather x 11 = $50 x 21 = $200 Cool Weather x 12 = $100 Warm Weather x 22 =$ Prentice-Hall, Inc. Chap 17-8 Opportunity Loss: Example Highest possible profit for an event E i - Actual profit obtained for an action A j Opportunity Loss (l ij ) Event: Cool Weather Action: Profit x 11 : $50 Alternative Action: Profit x 12 : $100 Opportunity Loss l 11 = $100 - $50 = $50 Opportunity Loss l 12 = $100 - $100 = $ Prentice-Hall, Inc. Chap 17-9
4 Chapter 17 Student Lecture Notes 17-4 Opportunity Loss: Table Alternative Course of Action Event Optimal Profit of Sell Sell Action Optimal Action Cool Hot = = 0 Weather Dogs Warm Soft = = 75 Weather Drinks 2004 Prentice-Hall, Inc. Chap Decision Criteria Expected Monetary Value (EMV) Expected profit for taking action Aj Expected Opportunity Loss (EOL) Expected loss for taking action Aj Expected Value of Perfect Information (EVPI) Expected opportunity loss from the best decision Return-to-Risk-Ratio Expected monetary value relative to the amount of risk (variation) 2004 Prentice-Hall, Inc. Chap Expected Monetary Value (EMV) = Sum (monetary payoffs of events) (probabilities of the events) Number of events ΕΜV j = N X ij P i Decision Criteria - EMV i = 1 EMV j = expected monetary value of action j X ij = payoff for action j and event i P i = probability of event i occurring 2004 Prentice-Hall, Inc. Chap 17-12
5 Chapter 17 Student Lecture Notes 17-5 Decision Criteria - EMV Table P i Event MV x ij P i MV x ij P i Soft Hot Drinks Dogs.50 Cool $50 $50.5 = $25 $100 $ = $50.50 Warm $200 $200.5 = 100 $125 $ = EMV Soft Drink = $125 EMV Hot Dog = $ Highest EMV = Better Alternative 2004 Prentice-Hall, Inc. Chap Decision Criteria - EOL Expected Opportunity Loss (EOL) = Sum (opportunity losses of events) (probabilities of events) N ΕΟL j = l ij P i i =1 EOL j = expected opportunity loss of action j l ij = opportunity loss for action j and event i P i = probability of event i occurring 2004 Prentice-Hall, Inc. Chap Decision Criteria - EOL Table P i Event Op Loss l ij P i Op Loss l ij Pi.50 Cool $50 $50.50 = $25 $0 $0.50 = $0.50 Warm 0 $0.50 = $0 $75 $75.50 = $37.50 EOL = $25 EOL = $37.50 Lowest EOL = Better Choice 2004 Prentice-Hall, Inc. Chap 17-15
6 Chapter 17 Student Lecture Notes 17-6 EVPI Expected Value of Perfect Information (EVPI) The expected opportunity loss from the best decision Expected Profit Under Certainty - Expected Monetary Value of the Best Alternative EVPI (should be a positive number) Represents the maximum amount you are willing to pay to obtain perfect information 2004 Prentice-Hall, Inc. Chap EVPI Computation Expected Profit Under Certainty =.50($100) +.50($200) = $150 Expected Monetary Value of the Best Alternative = $125 EVPI = $150 - $125 = $25 = Lowest EOL = The maximum you would be willing to spend to obtain perfect information 2004 Prentice-Hall, Inc. Chap Taking Account of Variability σ 2 for Soft Drink = (50-125) ( ) 2.5 = 5625 σ for Soft Drink = 75 CV for = (75/125) 100% = 60% σ 2 for = σ for = 12.5 CV for = (12.5/112.5) 100% = 11.11% 2004 Prentice-Hall, Inc. Chap 17-18
7 Chapter 17 Student Lecture Notes 17-7 Return-to-Risk Ratio Expresses the Relationship between the Return (Expected Payoff) and the Risk (Standard Deviation) EMV j RTRR = Return-to-Risk Ratio = σ j 1 RTRR = Return-to-Risk Ratio = CV j 2004 Prentice-Hall, Inc. Chap Return-to-Risk Ratio RTRR = 1/CV = 1.67 RTRR = 1/CV = 9 You might wish to choose. Although have the higher Expected Monetary Value, have a much larger return-torisk ratio and a much smaller CV Prentice-Hall, Inc. Chap Decision Making in PHStat PHStat Decision Making Expected Monetary Value Check the Expected Opportunity Loss and Measures of Variation boxes Excel Spreadsheet for the Food Vendor Example Microsoft Excel Worksheet 2004 Prentice-Hall, Inc. Chap 17-21
8 Chapter 17 Student Lecture Notes 17-8 Decision Making with Sample Information Permits Revising Old Probabilities Based on New Information Prior Probability New Information Revised Probability 2004 Prentice-Hall, Inc. Chap Revised Probabilities Additional Information: Weather forecast is COOL. When the weather has been cool, the forecaster has been correct 80% of the time. When it has been warm, the forecaster has been correct 70% of the time. F 1 = Cool forecast F 2 = Warm forecast Prior Probability E 1 = Cool weather = 0.50 E 2 = Warm weather = 0.50 P(F 1 E 1 ) = 0.80 P(F 1 E 2 ) = Prentice-Hall, Inc. Chap Revising Probabilities Revised Probability (Bayes Theorem) ( 1 1) PF ( 1 E2) ( 1) = 0.50 PE ( 2) = 0.50 PE ( 1) PF ( 1 E1) ( 1 1) PF ( 1) PE ( 2) PF ( 1 E2) ( 2 F1) PF ( ) PF E = 0.80 = 0.30 PE PE F = = =.73 PE = =.27 1 ( )( ) (.50)(.80) + (.50)(.30) 2004 Prentice-Hall, Inc. Chap 17-24
9 Chapter 17 Student Lecture Notes 17-9 Revised EMV Table P i Event Soft x ij P i Hot x ij P i Drinks Dogs.73 Cool $50 $36.50 $100 $73.27 Warm $ EMV Soft Drink = $90.50 EMV Hot Dog = $ Revised Probabilities Highest EMV = Better Alternative 2004 Prentice-Hall, Inc. Chap Revised EOL Table P i Event Op Loss l ij P i OP Loss l ij Pi Soft Drink.73 Cool $50 $36.50 $ Warm 0 $ EOL = EOL = $20.25 Lowest EOL = Better Choice 2004 Prentice-Hall, Inc. Chap Revised EVPI Computation Expected Profit Under Certainty =.73($100) +.27($200) = $127 Expected Monetary Value of the Best Alternative = $ EPVI = $127 - $ = $20.25 = The maximum you would be willing to spend to obtain perfect information 2004 Prentice-Hall, Inc. Chap 17-27
10 Chapter 17 Student Lecture Notes Taking Account of Variability: Revised Computation σ 2 for = ( ) ( ) 2.27 = σ for = CV for = (66.59/90.5) 100% = 73.6% σ 2 for = σ for = CV for = (11.10/106.75) 100% = 10.4% 2004 Prentice-Hall, Inc. Chap Revised Return-to-Risk Ratio RTRR = 1/CV = 1.36 RTRR = 1/CV = 9.62 You might wish to choose. have a much larger return-to-risk ratio Prentice-Hall, Inc. Chap Revised Decision Making in PHStat PHStat Decision Making Expected Monetary Value Check the Expected Opportunity Loss and Measures of Variation boxes Use the revised probabilities Excel Spreadsheet for the Food Vendor Example Microsoft Excel Worksheet 2004 Prentice-Hall, Inc. Chap 17-30
11 Chapter 17 Student Lecture Notes Utility Utility is the Idea that Each Incremental $1 of Profit Does Not Have the Same Value to Every Individual A risk averse person, once reaching a goal, assigns less value to each incremental $1. A risk seeker assigns more value to each incremental $1. A risk-neutral person assigns the same value to each incremental $ Prentice-Hall, Inc. Chap Three Types of Utility Curves Utility Utility Utility $ $ $ Risk Averter: Utility rises slower than payoff Risk Seeker: Utility rises faster than payoff Risk-Neutral: Maximizes expected payoff and ignores risk 2004 Prentice-Hall, Inc. Chap Chapter Summary Described the Payoff Table and Decision Trees Opportunity loss Provided Criteria for Decision Making Expected monetary value Expected opportunity loss Return-to-risk ratio Introduced Expected Profit Under Certainty Discussed Decision Making with Sample Information Addressed the Concept of Utility 2004 Prentice-Hall, Inc. Chap 17-33
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