Chapter3Chapter 3. Decision Analysis

Section 3.1. Decision Trees with Conditional Probabilities

Example 3.1 . P&G's Tide

Table 3.1. Given

New Product Payoff ($000)State of MarketSuccessfulFailureTide with Zonrox20.0-18.0Tide with Downy12.0-3.0Do nothing0.00.0Probability0.600.40

Table 3.2.AlternativeMaximum?EMVMarketProbabilityPayoffTide with ZonroxNo4.80Successful0.6020.0Failure0.40-18.0Tide with DownyYes6.00Successful0.6012.0Failure0.40-3.0Do nothingNo0.00Successful0.600.0Failure0.400.0Section 3.2. Decision Trees with Revised Probabilities

Example 3.2. P&G's Tide

Table 3.3. GivenP(Survey\Market)State of MarketSuccessfulFailurePositive0.800.25Negative0.200.75Prior Probability0.600.40Table 3.4.P(Survey\Market)State of MarketJoint ProbabilityP(Survey)SuccessfulFailureSuccessfulFailurePositive0.800.250.480.100.58Negative0.200.750.120.300.42P(Market\Survey)Prior ProbabilityPosterior ProbabilityTotalSuccessfulFailureSuccessfulFailurePositive0.600.400.830.171.00Negative0.600.400.290.711.00Example 3.3. P&G's Tide

Table 3.5. GivenNew Product Payoff ($000)State of MarketSuccessfulFailureTide with Zonrox20.0-18.0Tide with Downy12.0-3.0Do nothing0.00.0Prior Probability0.600.40Cost of Survey1.0Table 3.6.SurveyResultProbabilityProductMarketProbabilityPayoffConductPositive0.58Tide with ZonroxSuccessful0.8319.0Failure0.17-19.0Tide with DownySuccessful0.8311.0Failure0.17-4.0Do nothingSuccessful0.83-1.0Failure0.17-1.0Negative0.42Tide with ZonroxSuccessful0.2919.0Failure0.71-19.0Tide with DownySuccessful0.2911.0Failure0.71-4.0Do nothingSuccessful0.29-1.0Failure0.71-1.0NoneNone1.00Tide with ZonroxSuccessful0.6020.0Failure0.40-18.0Tide with DownySuccessful0.6012.0Failure0.40-3.0Do nothingSuccessful0.600.0Failure0.400.0Table 3.7.Decision 1Decision 2SurveyMaximum?EMVPlantMaximum?EMVConductYes7.34Tide with ZonroxYes12.45

Tide with DownyNo8.41

Do nothingNo-1.00

Tide with ZonroxNo-8.14

Tide with DownyYes0.29

Do nothingNo-1.00

NoneNo6.00Tide with ZonroxNo4.80

Tide with DownyYes6.00

Do nothingNo0.00

Table 3.8.SurveyEMVCostTotal

Conduct7.341.008.34None6.000.006.00EV of Sample Information (EVSI)2.34Section 3.3 Utility TheoryExample 3.4. Softdrink Companies

Table 3.9. GivenUtility TablePayoff ($000)CompanyCokePopPepsi-10.00.000.000.00-5.00.400.250.100.00.700.500.305.00.900.750.6010.01.001.001.00

Figure 3.1. Utility Curve

Table 3.10.

Propensity to Risk

CompanyPropensityCokePopPepsi

Example 3.5. Softdrink Companies

Table 3.11. Given

New Investment Payoff ($000)State of MarketSuccessfulFailureNew Product10.0-10.0New Plant5.0-5.0Do Nothing0.00.0Probability0.520.48Table 3.12.

New Investment Payoff ($000)State of MarketEMVMaximum?SuccessfulFailureNew ProductNew PlantDo NothingProbabilityMaximumDecisionTable 3.13.

CompanyCokePropensity to RiskNew Investment Payoff ($000)State of MarketUtilityEUVSuccessfulFailureSuccessfulFailureNew ProductNew PlantDo NothingProbabilityMaximumDecision

Table 3.14.

CompanyPopPropensity to RiskNew Investment Payoff ($000)State of MarketUtilityEUVSuccessfulFailureSuccessfulFailureNew ProductNew PlantDo NothingProbabilityMaximumDecisionTable 3.15.

CompanyPepsiPropensity to RiskNew Investment Payoff ($000)State of MarketUtilityEUVSuccessfulFailureSuccessfulFailureNew ProductNew PlantDo NothingProbabilityMaximumDecision