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

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Presentation on theme: "Chapter Topics The Payoff Table and Decision Trees Opportunity Loss Criteria for Decision Making Expected Monetary Value Return to Risk Ratio."— Presentation transcript:

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 Payoff TableDecision Tree Two Methods of Listing

4 Event (E i ) Cool Weather (E 1 ) x 11 =$50 x 12 = $100 Warm Weather (E 2 ) x 21 = 200 x 22 = 125 Payoff Table Consider a food vendor determining whether to sell soft drinks or hot dogs. Course of Action (A j ) Sell Soft Drinks (A 1 ) Sell Hot Dogs (A 2 ) x ij = payoff (profit) for event i and action j

5 Decision Tree:Example Soft Drinks Food Vendor Profit Tree Diagram Hot Dogs Cool Weather Warm Weather x 11 = $50 x 21 = 200 x 22 =125 x 12 = 100

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

7 Opportunity Loss: Table Event Optimal Profit of Sell Soft Drinks Sell Hot Dogs Action Optimal Action Cool Hot = = 0 Weather Dogs Warm Soft = = 75 Weather Drinks Alternative Course of Action

8 Decision Criteria Expected Monetary Value (EMV)  The expected profit for taking an action A j Expected Opportunity Loss (EOL)  The expected loss for not taking action A j 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) XijXij Pi Pi  V j   N EMV j = expected monetary value of action j x i,j = payoff for action j and event i P i = probability of event i occurring i = 1

10 Decision Criteria -- EMV Table Example: Food Vendor P i Event Soft x ij P i Hotx ij P i Drinks Dogs.50 Cool $50 $50 .5 = $25 $100 $100 .50 = $50.50 Warm $200 $200 .5 = 100 $125 $25 .50 = EMV Soft Drink = $125EMV Hot Dog = $ Better alternative

11 Decision Criteria -- EOL Expected Opportunity Loss (EOL) Sum (opportunity losses of events)  (probabilities of events)  L j   lijlij PiPi EOL j = expected monetary value of action j l i,j = payoff for action j and event i P i = probability of event i occurring i =1 N

12 Decision Criteria -- EOL Table Example: Food Vendor P i Event Op Loss l ij P i OP Loss l ij Pi 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  2 for Soft Drink = ( ) 2 .5 + ( ) 2 .5 = 5625  for Soft Drink = 75 CV for Soft Drinks = (75/125)  100% = 60%  2 for Hot Dogs =  for Hot dogs = 12.5 CV for 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 = RRR Soft Drinks = 125/75 = 1.67 RRR Hot 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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