Abstract: A method provides for an efficient unconstrained and nonlinear constrained optimization solution to a multivariate allocation of resources to meet manufacturing needs for uncertain multiproduct demand, where uncertainty is captured through a multivariate normal distribution over product demand (or more generally, through a member of the elliptical family of distributions).

Abstract: A method for the allocation of resources. A series of products (refinements) is arranged in a product space plan (PSP) according to connectivities between the products and associated components (resources). An expected value function is derived for the plan, and converted into a closed form expression. The PSP is transformed into a working space plan (WSP) having corresponding elements for each product. A loading step is applied to the WSP wherein each element is sequentially analyzed to determine if an associated component gates production of that product. Each element is loaded, with components being unloaded from prior elements if a subsequent element is gated. A reloading step redetermines if any elements are gated by a component that might have been unloaded from the element. If the element remains gated, the elements sharing the component are merged into a sub-plan, which can be maximized as a function of a single variable.

Abstract: A computer-implemented method is disclosed. The method includes producing optimized prices for products for sale.

Abstract: A method and apparatus providing for an efficient solution to the multivariate allocation of resources are described. A model is formulated that derives the relationship between a set of resources and a set of refinements, wherein any of a number of resources are used to build or comprise a refinement. The model provides for at least: the resource consumption as based upon the relationship between each refinement and its set of supporting resources, a demand distribution of the refinements, and a value function. Each resource, and the refinements that it supports, generates a resource hyperplane in a demand space, and the complete set of refinements generates an intersecting set of hyperplanes forming a polytope on which resource allocation fulfills refinement demand. An expected value function is thereafter formulated and transformed into a closed form solution.