Roll cutting problems and an application in paper production industry

This study addresses the roll cutting problem in the paper production industry, aiming to develop a mathematical model that minimizes trim loss and total raw material consumption while meeting customer demands. Roll cutting problems are a one-dimensional subclass of cutting stock problems, focusing on optimizing the process of cutting large paper rolls into smaller rolls tailored to customer requirements. In this study, a mixed-integer linear programming (MILP) approach was employed to optimize cutting planning, which is a critical part of production planning. The developed mathematical model was coded in Python and executed using Gurobi Solver. The study aims to generate optimal cutting patterns to fulfill customer demands of varying widths, particularly during periods of high order intensity, while minimizing trim waste generated from the cutting process. It offers flexible solutions such as parameter management, variability in the objective function, and the use of auxiliary (joker) rolls. Experimental tests and real-life case studies were conducted to evaluate the model's effectiveness across small, medium, large and very large-scale problems. The results demonstrate successful outcomes in terms of raw material utilization, trim loss minimization, and production efficiency, providing a valuable decision support system for cutting planning in the paper production industry. KEYWORDS: Roll cutting problems, cutting pattern minimization, trim loss minimization, mixed-Integer linear programming (MILP), paper industry