An analysis of the integrated lot-sizing and cutting-stock problem formulation

摘要

The integrated lot-sizing and cutting-stock problem has become a trend in the last decades for its applicability and advantage. Consequently, different approaches and formulations have been developed. One of them, which is widespread and related to the production and cutting process of paper, is the research subject of this paper. Fundamental considerations about the literature model are discussed and an alternative formulation is proposed, which consists of a simplified version that can provide better solutions. The upgrade modifications are proved analytically and an instance is analyzed to exemplify the discussed improvement. Moreover, computational tests are performed to compare both formulations. The novelty of the proposed formulation is the possibility of finding better solutions through the reduction of a constraint set, which guarantees the flexibility given by item and object inventories in meeting demand and it also enables a reduction in the total amount of produced paper. The proposed formulation has a significant impact on future research since the addressed model is the target of many scientific researches and practical applications.