Patent US 6,772,037

A pattern solution set for paper roll trimming to fulfill orders is generated using constraint programming and a heuristic. For every pattern generated, an objective function is evaluated based on the sum of waste factor and the variance of the quantity ordered for all widths in that pattern. The pattern that has the least objective function is chosen with the maximum number of sets possible. Orders are updated with the quantities left over and then the process continues, forming a solution tree, which serves as an initial solution set. The initial solution set is checked individually against the average loss of the solution set. Nodes in the solution tree having trim loss greater than the average loss are identified. Branches of the tree emanating from its parent are explored for better patterns. The process continues until all patterns are below the initial average loss.