© 2002 Prentice-Hall, Inc.Chap 17-1 Basic Business Statistics (8 th Edition) Chapter 17 Decision Making

© 2002 Prentice-Hall, Inc. Chap 17-2 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

© 2002 Prentice-Hall, Inc. Chap 17-3 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)

© 2002 Prentice-Hall, Inc. Chap 17-4 List Possible Actions or Events Payoff TableDecision Tree Two Methods of Listing

© 2002 Prentice-Hall, Inc. Chap 17-5 Payoff Table (Step 1) Consider a food vendor determining whether to sell soft drinks or hot dogs. Course of Action (A j ) Sell Soft Drinks (A 1 ) x ij = payoff (profit) for event i and action j Event (E i ) Cool Weather (E 1 ) x 11 =$50 x 12 = $100 Warm Weather (E 2 ) x 21 = $200 x 22 = $125 Sell Hot Dogs (A 2 )

© 2002 Prentice-Hall, Inc. Chap 17-6 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.”

© 2002 Prentice-Hall, Inc. Chap 17-7 Payoff Table (Step 2): Do Some Actions Dominate? (continued) Event (E i ) Level of Demand Course of Action (A j ) Production Process A B C D Low Moderate High Action C “dominates” Action D Action D is “inadmissible”

© 2002 Prentice-Hall, Inc. Chap 17-8 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

© 2002 Prentice-Hall, Inc. Chap 17-9 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 x 11 : $50 Alternative Action: Hot Dogs Profit x 12 : $100 Opportunity Loss l 11 = $100 - $50 = $50 Opportunity Loss l 12 = $100 - $100 = $0

© 2002 Prentice-Hall, Inc. Chap Event Optimal Profit of Sell Soft Drinks Sell Hot Dogs Action Optimal Action Cool Hot = = 0 Weather Dogs Warm Soft = = 75 Weather Drinks Opportunity Loss: Table Alternative Course of Action

© 2002 Prentice-Hall, Inc. Chap 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

© 2002 Prentice-Hall, Inc. Chap Expected Monetary Value (EMV) = Sum (monetary payoffs of events)  (probabilities of the events) Decision Criteria -- EMV X ij P i  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 Number of events

© 2002 Prentice-Hall, Inc. Chap Decision Criteria -- EMV Table Example: Food Vendor P i Event MV x ij P i MVx ij P i SoftHot Drinks Dogs.50 Cool $50 $50 .5 = $25 $100 $100 .50 = $50.50 Warm $200 $200 .5 = 100 $125 $125 .50 = EMV Soft Drink = $125 Highest EMV = Better alternative EMV Hot Dog = $112.50

© 2002 Prentice-Hall, Inc. Chap Decision Criteria -- EOL Expected Opportunity Loss (EOL) Sum (opportunity losses of events)  (probabilities of events)  L j   l ij PiPi EOL j = expected opportunity loss of action j l i,j = opportunity loss for action j and event i P i = probability of event i occurring i =1 N

© 2002 Prentice-Hall, Inc. Chap 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 Lowest EOL = Better Choice

© 2002 Prentice-Hall, Inc. Chap 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

© 2002 Prentice-Hall, Inc. Chap 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

© 2002 Prentice-Hall, Inc. Chap Taking Account of Variability Example: Food Vendor  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 = (12.5/112.5)  100% = 11.11%

© 2002 Prentice-Hall, Inc. Chap Return to Risk Ratio Expresses the relationship between the return (expected payoff) and the risk (standard deviation)

© 2002 Prentice-Hall, Inc. Chap 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.

© 2002 Prentice-Hall, Inc. Chap 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

© 2002 Prentice-Hall, Inc. Chap Decision Making with Sample Information Permits revising old probabilities based on new information New Information Revised Probability Prior Probability

© 2002 Prentice-Hall, Inc. Chap 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 F 1 = Cool forecast F 2 = Warm forecast E 1 = Cool Weather = 0.50 E 2 = Warm Weather = 0.50 P(F 1 | E 1 ) = 0.80 P(F 1 | E 2 ) = 0.30

© 2002 Prentice-Hall, Inc. Chap Revising Probabilities Example:Food Vendor Revised Probability (Bayes’s Theorem)

© 2002 Prentice-Hall, Inc. Chap Revised EMV Table Example: Food Vendor P i Event Soft x ij P i Hotx ij P i Drinks Dogs.73 Cool $50 $36.50 $100 $73.27 Warm $ EMV Soft Drink = $90.50 EMV Hot Dog = $ Highest EMV = Better alternative Revised probabilities

© 2002 Prentice-Hall, Inc. Chap Revised EOL Table Example: Food Vendor P i Event Op Loss l ij P i OP Loss l ij Pi Soft Drink Hot Dogs.73 Cool $50 $36.50 $00.27 Warm 0 $ EOL Soft Drinks = EOL Hot Dogs = $20.25 Lowest EOL = Better Choice

© 2002 Prentice-Hall, Inc. Chap Revised EVPI Computation Expected Profit Under Certainty =.73($100) +.27($200) = $127 Expected Monetary Value of the Best Alternative = $ EPVI = $127 - $ = $20.25 = The maximum you would be willing to spend to obtain perfect information

© 2002 Prentice-Hall, Inc. Chap Taking Account of Variability: Revised Computation  2 for Soft Drinks = ( ) 2 .73 + ( ) 2 .27 =  for Soft Drinks = CV for Soft Drinks = (66.59/90.5)  100% = 73.6%  2 for Hot Dogs =  for Hot dogs = CV for Hot dogs = (11.10/106.75)  100% = 10.4%

© 2002 Prentice-Hall, Inc. Chap Revised Return to Risk Ratio You might want to choose Hot Dogs. Hot Dogs have a much larger return to risk ratio.

© 2002 Prentice-Hall, Inc. Chap 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

© 2002 Prentice-Hall, Inc. Chap 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.

© 2002 Prentice-Hall, Inc. Chap Three Types of Utility Curves Utility $$$ Risk Averter: Utility rises slower than payoff Risk Seeker: Utility rises faster than payoff Risk-Neutral: Maximizes Expected payoff and ignores risk

© 2002 Prentice-Hall, Inc. Chap 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