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Decision Making with Payoff Analysis: A Food Vendor's Dilemma

Explore decision-making strategies using payoff tables, decision trees, and opportunity loss calculations with a case study of a food vendor choosing between selling hot dogs or soft drinks. Learn how to assess payoffs, determine optimal actions, and evaluate decision criteria for maximizing profit.

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Decision Making with Payoff Analysis: A Food Vendor's Dilemma

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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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