Patent ID: 8620729

Claim:
A robust method for solving in a programmed computer, optimization problems under uncertainty applicable to supply chain management in a multi-commodity, time-dependent setting having (i) one or more objective functions, each of the objective functions having one or more constraints, wherein the number of non-positivity constraints is typically smaller than the number of parameters, with one or more classes of uncertainty, (ii) input data represented in one or more ensembles with inputs being specified in one or more stages (iii) parameters based on the ensembles, (iv) one or more assumptions about a future, and (v) quantitative estimates of information within the input data and one or more solutions being generated by: a. Specifying the uncertainty as a hierarchical series of sets of constraints on parameters, with the parameters restricted to a constraint set forming an ensemble, and the hierarchy of constraints, represented as mathematical sets forming a hierarchy of ensemble, said hierarchy being based on subset, intersection or disjoint relationships by creating an ensemble with a specific optimal structure for supply chain management including nominal values for variables such as demand and input, the hierarchical series of sets of constraints on parameters represented in a storage element; b. Utilizing optimization techniques to identify minimum and maximum bounds on 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, the maximum and minimum bounds on each objective function represented in the storage element; c. Estimating a volume of candidate ensembles and relating the volume to one or more information theoretic measures; d. Utilizing information theoretic measures to analyze and iteratively refine the ensembles by changing a specificity of the bounds on the objective function; e. using a processor to perform transformations on the supply chain management structure to simulate perturbations on the variables within the optimal structure; and f. Maximizing or minimizing for a particular variable within the supply chain structure using linear programming.