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Chapter Topics

Chapter Topics. The Payoff Table and Decision Trees Opportunity Loss Criteria for Decision Making Expected Monetary Value Return to Risk Ratio. Features of Decision Making. List Alternative Courses of Action (Possible Events or Outcomes)

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Chapter Topics

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  1. Chapter Topics • The Payoff Table and Decision Trees • Opportunity Loss • Criteria for Decision Making • Expected Monetary Value • Return to Risk Ratio

  2. Features of Decision Making • List Alternative Courses of Action (Possible Events or Outcomes) • Determine ‘Payoffs’ (Associate a Payoff with Each Event or Outcome) • Adopt Decision Criteria (Evaluate Criteria for Selecting the Best Course of Action)

  3. List Possible Actions or Events Two Methods of Listing Payoff Table Decision Tree

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

  5. 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

  6. 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: $50 Alternative Action: Hot Dogs Profit: $100 Opportunity Loss = $100 - $50 = $50 Note: Opportunity Loss is always positive

  7. 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

  8. Decision Criteria • Expected Monetary Value (EMV) • The expected profit for taking an actionAj • Expected Opportunity Loss (EOL) • The expected loss for not taking actionAj • Expected Value of Perfect Information (EVPI) • The expected opportunity loss from the best decision

  9. Decision Criteria -- EMV • Expected Monetary Value (EMV) • Sum(monetary payoffs of events)´(probabilities of the events) N å EMVj= Xij Pi i = 1 EMVj = expected monetary value of action j xi,j= payoff for actionjand event i Pi = probability of eventioccurring

  10. Decision Criteria -- EMV Table Example: Food Vendor PiEvent Soft xijPi Hot xijPi Drinks Dogs .50 Cool $50 $50 ´.5 = $25 $100 $100´.50 = $50 .50 Warm $200 $200 ´.5 = 100 $125 $25´.50 = 62.50 EMV Soft Drink = $125 EMV Hot Dog = $112.50 Better alternative

  11. Decision Criteria -- EOL • Expected Opportunity Loss (EOL) • Sum(opportunity losses of events)´(probabilities of events) N å EOLj= lij Pi i =1 EOLj= expected monetary value of action j li,j = payoff for action j and eventi Pi = probability of event ioccurring

  12. 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 Better Choice

  13. Decision Criteria -- 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)

  14. EVPI Computation Expected Profit Under Certainty = .50($100) + .50($200) = $150 Expected Monetary Value of the Best Alternative = $125 EPVI = $25 The maximum you would be willing to spend to obtain perfect information.

  15. Taking Account of Variability: FoodVendor s2 for Soft Drink = (50 -125)2 ´.5 + (200 -125)2 ´.5 = 5625 s for Soft Drink = 75 CVfor Soft Drinks = (75/125) ´ 100% = 60% s2 for Hot Dogs = 156.25 s for Hot dogs = 12.5 CVfor Hot dogs = 11.11%

  16. Return to Risk Ratio Expresses the relationship between the return (payoff) and the risk (standard deviation). RRR = Return to Risk Ratio = RRRSoftDrinks = 125/75 = 1.67 RRRHot Dogs = 9 You might wish 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. Note: RRR is the inverse of CV

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