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Basic Business Statistics (8 th Edition)

Basic Business Statistics (8 th Edition). Chapter 17 Decision Making. 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

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Basic Business Statistics (8 th Edition)

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  1. Basic Business Statistics(8th Edition) Chapter 17 Decision Making © 2002 Prentice-Hall, Inc.

  2. 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 © 2002 Prentice-Hall, Inc.

  3. 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) © 2002 Prentice-Hall, Inc.

  4. List Possible Actions or Events Two Methods of Listing Payoff Table Decision Tree © 2002 Prentice-Hall, Inc.

  5. Payoff Table (Step 1) Consider a food vendor determining whether to sell soft drinks or hot dogs. Course of Action (Aj) Sell Soft Drinks (A1) Sell Hot Dogs (A2) Event (Ei) Cool Weather (E1) x11 =$50x12 = $100 Warm Weather (E2) x21 = $200 x22 = $125 xij = payoff (profit) for event i and action j © 2002 Prentice-Hall, Inc.

  6. 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.” © 2002 Prentice-Hall, Inc.

  7. Action C “dominates” Action D Action D is “inadmissible” Payoff Table (Step 2):Do Some Actions Dominate? (continued) Course of Action (Aj)Production Process Event (Ei) Level of Demand A B C D 70 80 100 100 120 120 125 120 200 180 160 150 Low Moderate High © 2002 Prentice-Hall, Inc.

  8. Decision Tree:Example Food Vendor Profit Tree Diagram x11 = $50 Cool Weather Warm Weather Soft Drinks x21 = $200 Hot Dogs x12 = $100 Cool Weather Warm Weather x22 =$125 © 2002 Prentice-Hall, Inc.

  9. Opportunity Loss: Example Highest possible profit for an event Ei - Actual profit obtained for an action Aj Opportunity Loss (lij) Event: Cool Weather Action: Soft Drinks Profit x11 : $50 Alternative Action: Hot Dogs Profit x12 : $100 Opportunity Loss l11 = $100 - $50 = $50 Opportunity Loss l12 = $100 - $100 = $0 © 2002 Prentice-Hall, Inc.

  10. Opportunity Loss: Table Alternative Course of Action Event Optimal Profit of Sell Soft Drinks Sell Hot Dogs Action Optimal Action Cool Hot 100 100 - 50 = 50 100 - 100 = 0 Weather Dogs Warm Soft 200 200 - 200 = 0 200 - 125 = 75 Weather Drinks © 2002 Prentice-Hall, Inc.

  11. Decision Criteria • Expected monetary value (EMV) • The expected profit for taking an action Aj • Expected opportunity loss (EOL) • The expected loss for taking action Aj • Expected value of perfect information (EVPI) • The expected opportunity loss from the best decision © 2002 Prentice-Hall, Inc.

  12. Decision Criteria -- EMV Expected Monetary Value (EMV) = Sum(monetary payoffs of events)  (probabilities of the events) Number of events N  Vj Xij Pi i = 1 EMVj = expected monetary value of action j Xi,j = payoff for action j and event i Pi = probability of event i occurring © 2002 Prentice-Hall, Inc.

  13. Decision Criteria -- EMV Table Example: Food Vendor PiEvent MV xijPi MV xijPi Soft Hot Drinks Dogs .50 Cool $50 $50 .5 = $25 $100 $100.50 = $50 .50 Warm $200 $200 .5 = 100 $125 $125.50 = 62.50 EMV Soft Drink = $125 EMV Hot Dog = $112.50 Highest EMV = Better alternative © 2002 Prentice-Hall, Inc.

  14. Decision Criteria -- EOL Expected Opportunity Loss (EOL) Sum (opportunity losses of events)  (probabilities of events) N  Lj lij Pi i =1 EOLj= expected opportunity loss of action j li,j = opportunity loss for action j and event i Pi = probability of event i occurring © 2002 Prentice-Hall, Inc.

  15. Decision Criteria -- EOL Table Example: Food Vendor PiEvent Op Loss lijPi Op Loss lijPi Soft Drinks Hot Dogs .50 Cool $50 $50.50 = $25 $0 $0.50 = $0 .50 Warm 0 $0 .50 = $0 $75 $75 .50 = $37.50 EOL Soft Drinks = $25 EOL Hot Dogs = $37.50 Lowest EOL = Better Choice © 2002 Prentice-Hall, Inc.

  16. EVPI • Expected value of perfect information (EVPI) • The expected opportunity loss from the best decision • Represents the maximum amount you are willing to pay to obtain perfect information Expected Profit Under Certainty - Expected Monetary Value of the Best Alternative EVPI (should be a positive number) © 2002 Prentice-Hall, Inc.

  17. 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 © 2002 Prentice-Hall, Inc.

  18. Taking Account of VariabilityExample: Food Vendor 2 for Soft Drink = (50 -125)2 .5 + (200 -125)2 .5 = 5625  for Soft Drink = 75 CVfor Soft Drinks = (75/125)  100% = 60% 2 for Hot Dogs = 156.25  for Hot dogs = 12.5 CVfor Hot dogs = (12.5/112.5)  100% = 11.11% © 2002 Prentice-Hall, Inc.

  19. Return to Risk Ratio Expresses the relationship between the return (expected payoff) and the risk (standard deviation) © 2002 Prentice-Hall, Inc.

  20. Return to Risk RatioExample: Food Vendor You might want to choose hot dogs. Although soft drinks have the higher Expected Monetary Value, hot dogs have a much larger return to risk ratio and a much smaller CV. © 2002 Prentice-Hall, Inc.

  21. Decision Making in PHStat • PHStat | decision-making | expected monetary value • Check the “expected opportunity loss” and “measures of valuation” boxes • Excel spreadsheet for the food vendor example © 2002 Prentice-Hall, Inc.

  22. Permits revising old probabilities based on new information Decision Making with Sample Information Prior Probability New Information Revised Probability © 2002 Prentice-Hall, Inc.

  23. Revised Probabilities Example: Food Vendor Additional Information: Weather forecast is COOL. When the weather is cool, the forecaster was correct 80% of the time. When it has been warm, the forecaster was correct 70% of the time. F1 = Cool forecast F2 = Warm forecast E1 = Cool Weather = 0.50 E2 = Warm Weather = 0.50 P(F1 | E1) = 0.80 P(F1 | E2) = 0.30 Prior Probability © 2002 Prentice-Hall, Inc.

  24. Revising Probabilities Example:Food Vendor • Revised Probability (Bayes’s Theorem) © 2002 Prentice-Hall, Inc.

  25. Revised EMV Table Example: Food Vendor PiEvent Soft xijPi Hot xijPi Drinks Dogs .73 Cool $50 $36.50 $100 $73 .27 Warm $200 54 125 33.73 EMV Soft Drink = $90.50 EMV Hot Dog = $106.75 Revised probabilities Highest EMV = Better alternative © 2002 Prentice-Hall, Inc.

  26. Revised EOL Table Example: Food Vendor PiEvent Op Loss lijPi OP Loss lijPi Soft Drink Hot Dogs .73 Cool $50 $36.50 $0 0 .27 Warm 0 $0 75 20.25 EOL Soft Drinks = 36.50 EOL Hot Dogs = $20.25 Lowest EOL = Better Choice © 2002 Prentice-Hall, Inc.

  27. Revised EVPI Computation Expected Profit Under Certainty = .73($100) + .27($200) = $127 Expected Monetary Value of the Best Alternative = $106.75 EPVI = $127 - $106.75 = $20.25 = The maximum you would be willing to spend to obtain perfect information © 2002 Prentice-Hall, Inc.

  28. Taking Account of Variability: Revised Computation 2 for Soft Drinks = (50 -90.5)2 .73 + (200 -90.5)2 .27 = 4434.75  for Soft Drinks = 66.59 CVfor Soft Drinks = (66.59/90.5)  100% = 73.6% 2 for Hot Dogs = 123.1875  for Hot dogs = 11.10 CVfor Hot dogs = (11.10/106.75)  100% = 10.4% © 2002 Prentice-Hall, Inc.

  29. Revised Return to Risk Ratio You might want to choose Hot Dogs. Hot Dogs have a much larger return to risk ratio. © 2002 Prentice-Hall, Inc.

  30. Revised Decision Makingin PHStat • PHStat | decision-making | expected monetary value • Check the “expected opportunity loss” and “measures of valuation” boxes • Use the revised probabilities • Excel spreadsheet for the food vendor example © 2002 Prentice-Hall, Inc.

  31. 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 $1. © 2002 Prentice-Hall, Inc.

  32. 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 © 2002 Prentice-Hall, Inc.

  33. 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 © 2002 Prentice-Hall, Inc.

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