Patent ID: 8032406

Claim:
A computer-implemented method of modeling, comprising: defining, by a computer, rules and constraints for product decision variables, wherein the product decision variables include assortment, space, inventory, placement, price and promotion; providing, by the computer, an objective function that utilizes the rules and constraints for the product decision variables; iteratively resolving, by the computer, the objective function into values which optimize sales, revenue, and profit for a retail business; and simultaneously optimizing, by the computer, the product decision variables including assortment, space, inventory, placement, price and promotion for the retail business by said iteratively resolving of the objective function into the values which optimize the sales, revenue, and profit for the retail business; wherein the objective function is max θ[{ x}]=π[{x},{us}]+λ ds DS[{us}]+λ im PI[{x}]+λ sa SA[{x }], and max θ is the maximized objective function π is profit x is a decision variable us is units sales λ ds is Lagrange multiplier or externally determined multiplier for dollar sales DS is dollar sales λ im is Lagrange multiplier or externally determined multiplier for price image PI is price image λ sa is Lagrange multiplier or externally determined multiplier for shelf area SA is shelf area.