Patent US 7,783,533

Selecting one or more entities from a plurality of candidate entities subject to one or more constraints is accomplished by establishing upper and lower profit-margin boundary values and determining an optimal profit-margin value within the boundary values using an iterative process. The iterative process includes one or more iterations of: setting a current profit-margin candidate based on a current upper profit-margin boundary value and a current lower profit-margin boundary value, determining whether the current profit-margin candidate value satisfies the constraint(s), adjusting the current upper or lower profit-margin boundary value based on the current profit-margin candidate value, and determining whether to use the current profit-margin candidate value as the optimal profit-margin value based the current upper profit-margin boundary value and the current lower profit-margin boundary value. The respective quantity for each of the candidate entities is then calculated based on the optimal profit-margin value.