Abstract: A robust method for solving in a computer, optimization problems under uncertainty including the steps of: specifying the uncertainty as a hierarchical series of sets of constraints on parameters, with the parameters restricted to each constraint set forming an ensemble, and the hierarchy of constraints, represented as mathematical sets forming a hierarchy of ensembles, said hierarchy being based on subset, intersection or disjoint relationships amongst them; utilizing optimization techniques to create effective identify minimum and maximum bounds on the each objective function, said bounds depending on the constraints comprising each ensemble of parameters and being computed for each of the assumptions about the future; estimating a volume of candidate ensembles and relating the volume to one or more information theoretic measures; and utilizing information theoretic measures to analyze and improve the candidate iteratively refine the ensembles and associated by changing a specificity of the bounds on the ob

Abstract: A robust method for solving in a computer, optimization problems under uncertainty including the steps of: specifying the uncertainty as a hierarchical series of sets of constraints on parameters, with the parameters restricted to each constraint set forming an ensemble, and the hierarchy of constraints, represented as mathematical sets forming a hierarchy of ensembles, said hierarchy being based on subset, intersection or disjoint relationships amongst them; utilizing optimization techniques to create effective identify minimum and maximum bounds on the each objective function, said bounds depending on the constraints comprising each ensemble of parameters and being computed for each of the assumptions about the future; estimating a volume of candidate ensembles and relating the volume to one or more information theoretic measures; and utilizing information theoretic measures to analyze and improve the candidate iteratively refine the ensembles and associated by changing a specificity of the bounds on the ob

Abstract: Modern decision support methods handle uncertainty or hypothesis about operating conditions, using one of two techniques viz. probabilistic formulation and constraints based method, which is the subject of the present invention. A large number of applications use linear constraints to specify uncertainty. These linear constraints are the set of linear inequalities, which are used to define the demand/supply in the area of supply chains. The set of linear inequalities forms a polytope, the volume of which represents the information content. The present invention deals with the application of computational geometrical methods to find the set theoretic relationship—subset, intersection and disjointness among the polytopes and then present a visualization technique to represent these relationships among polytopes. This invention proposes a decision support system and method to visualize the relationship among the polytopes to help with decision support.