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Chap17

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Published on November 16, 2007

Author: Spencer

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Basic Business Statistics (8th Edition):  Basic Business Statistics (8th Edition) Chapter 17 Decision Making Chapter Topics:  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 Features of Decision Making:  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) List Possible Actions or Events:  List Possible Actions or Events Payoff Table Decision Tree Two Methods of Listing Payoff Table (Step 1):  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) xij = payoff (profit) for event i and action j Event (Ei) Cool Weather (E1) x11 =$50 x12 = $100 Warm Weather (E2) x21 = $200 x22 = $125 Sell Hot Dogs (A2) Payoff Table (Step 2): Do Some Actions Dominate?:  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.” Payoff Table (Step 2): Do Some Actions Dominate?:  Payoff Table (Step 2): Do Some Actions Dominate? (continued) Event (Ei) Level of Demand Course of Action (Aj) Production Process A B C D Low Moderate High 70 80 100 100 120 120 125 120 200 180 160 150 Action C “dominates” Action D Action D is “inadmissible” Decision Tree: Example:  Decision Tree: Example Soft Drinks Food Vendor Profit Tree Diagram Hot Dogs Cool Weather Cool Weather Warm Weather Warm Weather x11 = $50 x21 = $200 x22 =$125 x12 = $100 Opportunity Loss: Example:  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 Opportunity Loss: Table:  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 Opportunity Loss: Table Alternative Course of Action Decision Criteria:  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 Decision Criteria -- EMV:  Expected Monetary Value (EMV) = Sum (monetary payoffs of events)  (probabilities of the events) Decision Criteria -- EMV Xij Pi Vj   N EMVj = expected monetary value of action j Xi,j = payoff for action j and event i Pi = probability of event i occurring i = 1 Number of events Decision Criteria -- EMV Table Example: Food Vendor:  Decision Criteria -- EMV Table Example: Food Vendor Pi Event 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 Highest EMV = Better alternative EMV Hot Dog = $112.50 Decision Criteria -- EOL:  Decision Criteria -- EOL Expected Opportunity Loss (EOL) Sum (opportunity losses of events)  (probabilities of events) Lj   lij Pi EOLj = expected opportunity loss of action j li,j = opportunity loss for action j and event i Pi = probability of event i occurring i =1 N Decision Criteria -- EOL Table Example: Food Vendor :  Decision Criteria -- EOL Table Example: Food Vendor Pi Event 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 EVPI:  Expected Profit Under Certainty - Expected Monetary Value of the Best Alternative EVPI (should be a positive number) 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 EVPI Computation:  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 Taking Account of Variability Example: Food Vendor:  Taking Account of Variability Example: 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% Return to Risk Ratio:  Return to Risk Ratio Expresses the relationship between the return (expected payoff) and the risk (standard deviation) Return to Risk Ratio Example: Food Vendor:  Return to Risk Ratio Example: 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. Decision Making in PHStat:  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 Decision Making with Sample Information:  Decision Making with Sample Information Permits revising old probabilities based on new information New Information Revised Probability Prior Probability Revised Probabilities Example: Food Vendor:  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. Prior Probability 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 Revising Probabilities Example:Food Vendor:  Revising Probabilities Example:Food Vendor Revised Probability (Bayes’s Theorem) Revised EMV Table Example: Food Vendor:  Revised EMV Table Example: Food Vendor Pi Event 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 Highest EMV = Better alternative Revised probabilities Revised EOL Table Example: Food Vendor :  Revised EOL Table Example: Food Vendor Pi Event 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 Revised EVPI Computation:  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 Taking Account of Variability: Revised Computation:  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% Revised Return to Risk Ratio:  Revised Return to Risk Ratio You might want to choose Hot Dogs. Hot Dogs have a much larger return to risk ratio. Revised Decision Making in PHStat:  Revised Decision Making in 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 Utility:  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. Three Types of Utility Curves:  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 Chapter Summary:  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

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