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Published byJewel Henshall Modified about 1 year ago

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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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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)

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List Possible Actions or Events Payoff TableDecision Tree Two Methods of Listing

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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)

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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.

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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%

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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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