DIFFERENT FORMULATIONS FOR SOLVING TRIM LOSS PROBLEMS IN A PAPER-CONVERTING MILL WITH ILP

In the present paper, trim loss problems connected to the paper-conver ting industry are analyzed and solved. The objective is to produce a s et of paper rolls from storage rolls such that a cost function includi ng the minimization of the trim loss as well as the time for cutting i s considered. The problem is a non-convex integer non-linear programmi ng (INLP) problem, due to its bilinear constraints. The problem can, h owever, be written in an expanded linear form and can, thus, be solved as an integer linear programming (ILP) or a mixed integer linear prog ramming (MILP) problem. The linear formulation is attractive from the point of view of formality. One drawback of linear formulations is the increased number of variables and constraints they give rise to. It i s, though, of interest to compare different ways of describing the pro blem as an ILP/MILP problem. There has previously been some academic i nterest in solving trim loss problems as linear programming problems. In this paper, we will present a general INLP formulation, some ways t o formulate and solve it as an ILP or MILP problem and compare the eff iciency of these different approaches. The examples considered are tak en from real daily trim optimization problems encountered at a Finnish paper-converting mill with a capacity of 100,000 tons/year.