Interactive multiobjective optimization under uncertainty

Article Abstract:

The unique difficulties that arise in constrained optimization problems due to uncertainty are often compounded by multiple, often contradictory, criteria. The difficulty of multi-objective optimization problems arises from risky situations that require the analysis of different outcomes arising from multiple criteria and/or probabilistic states of nature. An interactive process based on the theory and methodology of the Geoffrion, Dyer, and Feinberg method and the Paired Comparison Method and utilizing a general multi-objective algorithm is proposed which accommodates uncertainty. The process is developed using a two-stage mathematical programming model to optimize constrained multiple objective problems under uncertainty and is appropriate for multiple criteria frameworks with a limited number of states of nature.

Research, Multiple criteria decision making, Mathematical optimization, Optimization theory

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Improving the Consistency of Conditional Probability Assessments for Forecasting and Decision Making

Article Abstract:

The causal versus diagnostic and the positive versus the negative relationship of events affect conditional probability assessment. The value of a joint probability table (JPT) is discussed. Credit scoring of loan applications and predicting the likelihood that the Dow Jones Industrial Index would be in a certain range on a certain date, Gross National Product (GNP) would have a specified growth rate in a six month period and a certain combination of the Dow Jones Index and GNP, are examples presented. The results are shown in tables and the use of JPT evaluated. Many consistency violations of the probability calculus are errors of cognitive biases in responses. A psychological experiment is suggested as desirable.

Management science, Forecasting, Decision support systems, Decision theory, Decision Support Software, Decision Making, Probability

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Assessing Scenario Probabilities Via Interactive Goal Programming

Article Abstract:

A goal programming approach is used for probability assessment as a basis for corporate planning decisions. This method entails interactive implementation which provides information about the relationships between the assessed conditional event and the scenario probabilities. A small numerical example illustrates the procedures for scenario analysis. A minmax objective is used to obtain an initial solution. Prioritized linear objectives and other constraints are shown. Pairwise conditional probability judgments and feasibility constraints are part of the linear goal programming framework.

Methods, Decision-making, Decision making, Analysis, Linear programming, Evaluation, Probabilities, Probability theory

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