Abstract: A method and structure for a computerized method for providing an optimization solution, includes, for a process, wherein is defined a linear functional form y=f(X,c), where X comprises a set of independent variables X={x1, . . . xn}, c includes a set of functional parameters c={c1, . . . cn}, and y comprises a dependent variable, where the independent variables set X is partitioned into two subsets, X1 and X2, receiving data for the process and minimizing y with respect to X1. Dependent variable y is maximized with respect to X2, subject to a set of constraints. The maximizing y includes a global optimum for the process.

Abstract: The present invention provides a method and apparatus for developing an optimal sales plan for multiple products with multiple price classes contingent on different possible realizations of uncertain demand over multiple time periods with the objective of maximizing expected revenue over a constrained capacity. The present invention formulates a multistage stochastic program that generates a quantity of each of the multiple products to be sold in each of the multiple time periods and a recommendation for when realized demand for at least one of the multiple time periods exceeds a planned sales volume; estimates a likelihood that the realized demand for the at least one of the multiple time periods exceeds the planned sales volume; and collects realized order data for each of the multiple time periods; and executes the multistage stochastic program using the likelihood and the realized order data to generate a sales plan.

Abstract: A method and structure for a computerized method for providing an optimization solution, includes, for a process, wherein is defined a linear functional form y=f (X,c), where X comprises a set of independent variables X={x1, . . . xn}, c includes a set of functional parameters c={c1, . . . cn}, and y comprises a dependent variable, where the independent variables set X is partitioned into two subsets, X1 and X2, receiving data for the process and minimizing y with respect to X1. Dependent variable y is maximized with respect to X2, subject to a set of constraints. The maximizing y includes a global optimum for the process.

Abstract: The present invention provides a method and apparatus for developing an optimal sales plan for multiple products with multiple price classes contingent on different possible realizations of uncertain demand over multiple time periods with the objective of maximizing expected revenue over a constrained capacity. The present invention formulates a multistage stochastic program that generates a quantity of each of the multiple products to be sold in each of the multiple time periods and a recommendation for when realized demand for at least one of the multiple time periods exceeds a planned sales volume; estimates a likelihood that the realized demand for the at least one of the multiple time periods exceeds the planned sales volume; and collects realized order data for each of the multiple time periods; and executes the multistage stochastic program using the likelihood and the realized order data to generate a sales plan.