Optimization of the cutting process integrated to the lot sizing in multi-plant paper production industries

Many industrial production and cutting processes have costs associated with setup, production of objects, waste of material in the cutting process, inventory, and transport which can vary according to each plant's location (factory). The production lot sizing, the planning of cuts, and the transport between plants of a company are interconnected problems that, if optimized in an integrated way, can lead to reduction in total costs. In the literature, such problems are widely addressed independently. Recently, the integrated lot sizing and cutting stock problem has been the subject of several studies. However, none have addressed the integrated problem, which also considers multiple plants. This paper presents an integer linear programming formulation for the integrated lot sizing and cutting stock problem with multiple plants and a solution methodology. The formulation is inspired by a practical situation in the paper-making industry. The developed solution methodology consists of a column generation method and a relax-and-fix with a feasibility heuristic. Computational tests were performed to evaluate the performance of the proposed approach and the solution methodology. The proposed approach presented lower total costs, demonstrating the potential for reducing all considered costs. The applied solution methodology showed satisfactory performance for all the studied instances.