Statistics for Managers Using Microsoft Excel Chapter 5 Decision Making
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1 Statistics for Managers Using Microsoft Excel Chapter 5 Decision Making 1999 Prentice-Hall, Inc. Chap. 5-1
2 Chapter Topics The Payoff Table and Decision Trees Opportunity Loss Criteria for Decision Making Expected Monetary Value Expected Profit Under Certainty Return to Risk Ratio Decision Making with Sample Information Utility 1999 Prentice-Hall, Inc. Chap. 5-2
3 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) 1999 Prentice-Hall, Inc. Chap. 5-3
4 List Possible Actions or Events Two Methods of Listing Payoff Table Decision Tree 1999 Prentice-Hall, Inc. Chap. 5-4
5 Payoff Table Consider a food vendor determining whether to sell soft drinks or hot dogs. Event (E i ) Course of Action (A j ) Sell Soft Drinks (A 1 ) Sell Hot Dogs (A 2 ) Cool Weather (E 1 ) x 11 =$50 x 12 = $100 Warm Weather (E 2 ) x 21 = 200 x 22 = 125 x ij = payoff (profit) for event i and action j 1999 Prentice-Hall, Inc. Chap. 5-5
6 Decision Tree:Example Food Vendor Profit Tree Diagram x 11 = $50 x 21 = 200 x 12 = 100 x 22 = Prentice-Hall, Inc. Chap. 5-6
7 Event: Cool Weather Opportunity Loss: Example Highest possible profit for an event E i - Actual profit obtained for an action A j Opportunity Loss (l ij ) Action: Soft Drinks Profit: $50 Alternative Action: Hot Dogs Profit: $100 Opportunity Loss = $100 - $50 = $ Prentice-Hall, Inc. Chap. 5-7
8 Opportunity Loss: Table Alternative Course of Action Event Optimal Profit of Sell Soft Drinks Sell Hot Dogs Action Optimal Action Cool Hot = = 0 Weather Dogs Warm Soft = = 75 Weather Drinks 1999 Prentice-Hall, Inc. Chap. 5-8
9 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 1999 Prentice-Hall, Inc. Chap. 5-9
10 Decision Criteria -- EMV Expected Monetary Value (EMV) Sum (monetary payoffs of events) (probabilities of the events) N EMV j = i = 1 X ij P i 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 1999 Prentice-Hall, Inc. Chap. 5-10
11 Decision Criteria -- EMV Table Example: Food Vendor P i Event Soft x ij P i Hot x ij P i Drinks Dogs.50 Cool $50 $50.5 = $25 $100 $ = $50.50 Warm $200 $200.5 = 100 $125 $25.50 = EMV Soft Drink = $125 EMV Hot Dog = $ Better alternative 1999 Prentice-Hall, Inc. Chap. 5-11
12 Decision Criteria -- EOL Expected Opportunity Loss (EOL) Sum (opportunity losses of events) (probabilities of events) N EOL j = l ij P i i =1 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 1999 Prentice-Hall, Inc. Chap. 5-12
13 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 1999 Prentice-Hall, Inc. Chap. 5-13
14 Decision Criteria -- EVPI Expected Value of Perfect Information (EVPI) The expected opportunity loss from the best decision Expected Profit Under Certainty - Expected Monetary Value of the Best Alternative EVPI (should be a positive number) Represents the maximum amount you are willing to pay to obtain perfect information 1999 Prentice-Hall, Inc. Chap. 5-14
15 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 Prentice-Hall, Inc. Chap. 5-15
16 Taking Account of Variability: FoodVendor s 2 for Soft Drink = (50-125) ( ) 2.5 = 5625 s for Soft Drink = 75 CV for Soft Drinks = (75/125) 100% = 60% s 2 for Hot Dogs = s for Hot dogs = 12.5 CV for Hot dogs = 11.11% 1999 Prentice-Hall, Inc. Chap. 5-16
17 Return to Risk Ratio Expresses the relationship between the return (payoff) and the risk (standard deviation). RRR = Return to Risk Ratio = EMV j s 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. j 1999 Prentice-Hall, Inc. Chap. 5-17
18 Decision Making with Sample Information Permits Revising Old Probabilities Based on New Information Prior Probability New Information Revised Probability 1999 Prentice-Hall, Inc. Chap. 5-18
19 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. F 1 = Cool forecast F 2 = Warm forecast Revised Probabilities Example: Food Vendor E 1 = Cool Weather = 0.50 E 2 = Warm Weather = 0.50 Prior Probability P(F 1 E 1 ) = 0.80 P(F 1 E 2 ) = Prentice-Hall, Inc. Chap. 5-19
20 Revising Probabilities Example:Food Vendor Revised Probability P(F 1 E 1 ) = 0.80 P(F 1 E 2 ) = 0.30 E 1 = 0.50 E 2 = 0.50 P(E 1 F 1 ) = P(cool) P( cool forecast cool) P(cool forecast) (.50) (.80) = =.73 (.80)(.50) + (.30)(.50) P(warm) P(cool forecast warm) P(E 2 F 1 ) = =.27 P(cool forecast) 1999 Prentice-Hall, Inc. Chap. 5-20
21 Revised EMV Table Example: Food Vendor P i Event Soft x ij P i Hot x ij P i Drinks Dogs.73 Cool $50 $36.50 $100 $73.27 Warm $ EMV Soft Drink = $90.50 EMV Hot Dog = $ Better alternative 1999 Prentice-Hall, Inc. Chap. 5-21
22 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 $ Warm 0 $ EOL Soft Drinks = EOL Hot Dogs = $20.25 Better Choice 1999 Prentice-Hall, Inc. Chap. 5-22
23 Revised EVPI Computation Expected Profit Under Certainty =.73($100) +.27($200) = $127 Expected Monetary Value of the Best Alternative = $ EPVI = $20.25 The maximum you would be willing to spend to obtain perfect information Prentice-Hall, Inc. Chap. 5-23
24 Taking Account of Variability: Revised Computation s 2 for Soft Drinks = ( ) ( ) 2.27 = s for Soft Drinks = CV for Soft Drinks = (66.59/90.5) 100% = 73.6% s 2 for Hot Dogs = s for Hot dogs = CV for Hot dogs = (11.10/106.75) 100% = 10.4% 1999 Prentice-Hall, Inc. Chap. 5-24
25 Revised Return to Risk Ratio Expresses the relationship between the return (payoff) and the risk (standard deviation). RRR = Return to Risk Ratio = EMV j s j RRR Soft Drinks = 90.50/66.59 = 1.36 RRR Hot Dogs = 9.62 You might wish to choose Hot Dogs. Hot Dogs have a much larger return to risk ratio Prentice-Hall, Inc. Chap. 5-25
26 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 $ Prentice-Hall, Inc. Chap. 5-26
27 Chapter Summary Described The Payoff Table and Decision Trees Opportunity Loss Provided Criteria for Decision Making Expected Monetary Value Expected Profit Under Certainty Return to Risk Ratio Discussed Decision Making with Sample Information Addressed the Concept of Utility 1999 Prentice-Hall, Inc. Chap. 5-27
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