Integrated lot-sizing and cutting stock problem applied to the mattress industry

In many productive processes, two important problems arise in the production planning: the lot-sizing problem and the cutting stock problem. Generally, companies deal with these problems separately but, by considering them in an integrated way, better results can be obtained. In this paper, the integrated lot-sizing and three-dimensional cutting stock problem applied to the mattress industry is investigated, aiming at reducing costs and waste. A mathematical model of mixed integer programming was proposed and solved with an optimisation package. Computational tests based on data collected at a mattress factory were carried out, allowing the comparison of the solutions proposed by the model and the solutions adopted by the factory. Additional tests were performed with random data in order to evaluate the behaviour of the model for different cases. The results indicate that the model performs well, reducing the objective function costs for different data sets. Based on the results, some interesting options can be explored by the industry; for example, by increasing the number of cutting patterns up to a certain level, the number of possible combinations for cutting is increased, resulting in better use of the material and a consequent reduction in costs.