in the future into present net value or worth. For economic values this time- 

 preference model is used to account for discount rates and inflation. The 

 objectives of the deterministic phase are: 1) to determine whether particular 

 alternatives are deterministically dominated, i.e., they always have a lower 

 worth than some other alternative, regardless of what values are selected for 

 the state variables; and 2) to determine which of the decision variables (table 

 1) and the state, or environmental, variables are most influential in affecting 

 the worth of each alternative. 



The probabilistic phase of the decision analysis focuses on resolving the 

 uncertainty in value or worth of any alternative. This uncertainty arises from 

 those (aleatory) state variables to which the worth of the alternatives is 

 found during the deterministic phase to be most sensitive. Probability dis- 

 tributions must be assigned to these aleatory variables over their potential 

 ranges of values. The structural model is expanded to include the probabilistic 

 values for the aleatory variables and the expected outcomes, expected values, 

 and expected worth are then calculated by the structural model, value model, 

 and time-preference model, respectively, based on the assigned probabilities. 

 A probabilistic sensitivity analysis then reveals whether one or more alterna- 

 tives are stochastically dominated, i.e., whether a particular alternative 

 always has a lower probability of achieving any specified worth than another 

 alternative, over the entire range of potential worth. Stochastically dominated 

 alternatives may be dismissed from further consideration because they consistently 

 have lower probable worth and are logically excluded. If certain alternatives 

 prove not to be stochastically dominated, then there is a logical risk in 

 selection of any alternative, and risk preference (Matheson and Howard 1968) 

 must be modeled for the decisionmaker (s ) or his surrogate. The risk-preference 

 model translates the expected worth under uncertainty into a certain worth 

 equivalent. The certain worth equivalent may be viewed as the smallest offered 

 certain worth that would induce a risk-averse decisionmaker to prefer another 

 alternative in place of one with uncertain outcomes and therefore an uncertain 

 worth. At this stage of the analysis, the optimal alternative, the one with 

 the highest certain equivalent worth, has been identified. 



The informational phase of the decision analysis focuses on determining 

 how much one should pay to upgrade the quality of information available for the 

 analysis prior to making the final decision. In effect the nature of the 

 information to be gained from a particular experimental program is anticipated, 

 with an associated cost, and the decision analysis models are then restructured 

 about that information, with its new (expected) attendant uncertainties. The 

 deterministic and probabilistic phases of the analysis are repeated for this 

 "new" information, and the optimal alternative is again identified with its new 

 certain equivalent worth. The value of the information is exactly that cost of 

 the experimental program which would make the certain equivalent worth of the 

 decision with the improved information just equal to that of the decision 

 without the information. This process is repeated for each of the aleatory 

 variables, separately and in combination, for which improved information might 

 be obtained. Where the value of the information exceeds the cost of the 

 experimental program (including the costs of the delay in the decision), then 

 the decision to gather new information is supported (fig. 3) and the analysis 

 should be reiterated on the basis of the improved information. When further 

 information gathering is projected to be overly costly, then the decisionmaker 

 is ready to act. 



17 



