Some Efficient Formulations for the Simultaneous Solution of Trim-Loss and Scheduling Problems in the Paper-Converting Industry

A production optimization problem concerned with the paper-converting industry is considered in the present paper. The problem can be written as a cost minimization or as a profit maximization problem. The problem is to produce a set of product paper reels from larger raw paper reels such that certain specifications are satisfied, while the overall objective function is minimized/maximized. In this formulation, both the widths and lengths of the different raw paper used are utilized as variables. The lengths as well as the ordered amounts of the product paper reels are allowed to vary within certain specified limits. In addition to the trim-loss constraints, constraints for the simultaneous sequential scheduling of the cutting machines is also included, giving time constraints for the cutting machines in the considered formulation. The income from the product paper and overproduction as well as costs derived from the raw paper used, machine time, format changes as well as knife changes are all included in the objective function. A numerical example from the paper-converting industry under consideration is included to illustrate the proposed procedure.