Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges

We discuss cutting stock problems (CSPs) from the perspective of the paper industry and the financial impact they make. Exact solution approaches and heuristics have been used for decades to support cutting stock decisions in that industry. We have developed polylithic solution techniques integrated in our ERP system to solve a variety of cutting stock problems occurring in real world problems. Among them is the simultaneous minimization of the number of rolls and the number of patterns while not allowing any overproduction. For two cases, CSPs minimizing underproduction and CSPs with master rolls of different widths and availability, we have developed new column generation approaches. The methods are numerically tested using real world data instances. An assembly of current solved and unsolved standard and non-standard CSPs at the forefront of research are put in perspective.