(125b) Quality-Based Retrimming Optimization

The trim-loss or cutting-stock problem in the paper industry evolves when a Jumbo-reel is cut into smaller rolls, which are either end-customer rolls or intermediate product rolls to be further processed (for instance through printing, coating or cutting). Standard trim-loss problem formulations consider given set of rolls and a set of jumbo-reels of uniform quality, i.e. no quality deviations are considered when generating the cutting patterns. Since the trim-loss problem generally contains logical decisions, combinatorial explosion of the optimization problem is often encountered. Due to this, heuristic-mathematical programming approaches are applied to solve the problem efficiently but not guaranteeing a global optimal solution. These include rounding heuristics, column generation, solving problem only partially and other knapsack-type of algorithms.

As the initial trim-loss problem is often solved as a part of the production planning already before the jumbo-reels are actually produced, the quality and defect data from various on-line sources along the paper machine have not been included. Based on this actual quality, it may happen that the initial cutting plan is far from optimal, for instance a high-value roll has been positioned on a location with severe quality defects. In order to overcome this type of problems, typically manual retrimming actions can be carried out. Here, we introduce a mathematical programming formulation for solving the re-trimming problem automatically. The approach results in optimal or at least close-to-optimal solutions with the effect of a significant reduction in quality loss, that is, the economical loss based on degraded quality.

In the method discussed, the exact geometrical position, as well as the quality information is taken into account. In order to be able to solve the problem within a few seconds, a two-step algorithmic approach is applied. This also allows to overcome the non-convexities of the original problem and ensures that the solution obtained is at least close-to-optimal. In this context, a close relationship to scheduling methodologies can be identified. Example cases are solved using ILOG-CPLEX and the results show that quality losses may be significantly reduced, which results in higher throughput, less reclamations and improved customer satisfaction, leading to significant savings in a paper mill.