A model for scheduling cutting operations in paper-converting processes

A practical instance of a one-dimensional cutting stock problem arising fre quently in the paper industry is considered. Given a set of raw paper rolls of known length and width, a set of product paper rolls of known length (e qual to the length of raw paper rolls) and width, practical cutting constra ints on a single cutting machine, and demand orders for all products, the p roblem requires the determination of an optimal cutting schedule to maximiz e the overall cutting process profitability while satisfying all demands an d cutting constraints. A purely mixed-integer linear programing (MILP) mode l is developed that does not require the a priori determination of all feas ible cutting combinations. A complex objective function including trim loss , overproduction, knife (pattern) changeover costs, and format (raw materia l type) changeover costs is optimized. A salient feature of the model is th at intermediate demand orders are taken into consideration as an integral p art of the formulation. A number of example problems, including an industri al case study, are employed to illustrate the applicability and computation al performance of the proposed method.