Method and apparatus for optimizing a multivariate allocation of resources

A computer-implemented method performed by a computer comprising:

• optimizing by the computer a multivariate representation of resources using multiple single-variable optimizations, wherein the resources are used in producing a set of products, and the resources, the set of products and their respective connectivities are represented in a product space plan, the optimizing comprising
• converting a non-linear expected value function associated with the resources and products into a closed form expression;
• transforming the product space plan into a working transformed space plan wherein:
• the products are transformed into working elements,
• the transforming step involves taking a transformation of the product space to provide the working transformed space,
• the distribution induced on the resources is transformed into a distribution with zero mean and unit variance, and
• the transformation includes an inverse Cholesky transformation of the product space to provide the working transformed space;
• performing a loading step to form elemental blocks as a function of a single variable of the multivariate representation with elements being loaded with resources that gate production of the element;
• examining the elemental blocks to determine if a first element has not been loaded with a corresponding first resource that gates production of the first element;
• if the examining indicates that the first element has not been loaded with the first resource, performing a re-loading step to form elemental blocks as a function of a single variable of the multivariate representation with the first element being reloaded with the first resource;
• solving by the computer for the maximum of each elemental block over each associated single variable of the multivariate representation;
• and
• determining and presenting the optimum level of resources as a function of the solved for maximums.