A Bi-Integrated Model for coupling lot-sizing and cutting-stock problems

The lot-sizing and cutting-stock problems arise, in general, in manufacturing industries as subsequent processes. Many authors have addressed these problems separately; however, some studies have considered integrated approaches to these problems in recent practical applications. This paper aims to introduce a new model for integrated lot-sizing, one-dimensional cutting-stock and two-dimensional cutting-stock problems. This integrated model can be used to address the papermaking process as a three-phase subsequent process, which starts from the production of jumbos and ends with the paper sheets used in daily life. The first phase of the process is modeled according to a lot-sizing problem, where the quantities of jumbos are determined to meet the demand of the entire planning horizon. The second phase is modeled as a one-dimensional cutting-stock problem, where the jumbos are cut into smaller reels. The reels are used as raw material for the third phase of the process, where they are cut again into sheets employing a two-dimensional cutting-stock problem. A heuristic algorithm that uses the column generation and relax-and-fix techniques is applied to evaluate the proposed model from a series of experiments. Gains of up 16.5% were observed compared to the solution obtained with no integration among the production phases. Additional analyses of the model behavior under multiple scenarios resulted in significant findings, as the increasing costs’ reduction as more product types are considered and the use of more efficient cutting patterns resulting in reduced material waste.