IMPACT OF RECTANGLE PRIORITIZATION ON RAW MATERIAL CONSUMPTION AND CUTTING TIME

In the two-dimensional rectangular strip packing problem (2D-SPP), a strip with an infinite dimension (height or width) must be cut into a predefined set of rectangles, seeking to find a packing layout that minimizes the infinite dimension. 2D-SPP is widely found in industries such as steel, wood, paper and glass, allowing the modeling of real scenarios and contributing to more efficient production processes. Furthermore, in industrial applications, the definition of packing layouts can increase competitiveness, promoting leaner and more agile processes. However, for the layouts to be applicable in real production environments, it is necessary to consider specific constraints and objectives, including prioritizing items and minimizing the time required to cut the rectangles. In this context, the objective of this work is to develop a mathematical model that minimizes the height obtained in the packing layout, considering the prioritization of rectangles by levels, in which rectangles with the same priority must be allocated to the same level. Despite increasing the expenditure of raw material, the packing layout based on levels can reduce the lead time, defined as the total time required to cut all the rectangles of a given group, simulating the release of the rectangles with the same priority immediately after cutting for the subsequent stages of production. Thus, integer linear programming mathematical model was developed, considering the prioritization of the rectangles and the calculation of the lead time per group, applied in 20 instances from the literature. The results obtained were compared with the model proposed by Kenmochi et al. (2009), which does not address the prioritization or the restriction of packing by levels. A trade-off between the models was found, such that the model with prioritization by levels increased the consumption of raw material in most instances, but significantly reduced the lead time of the groups of rectangles with higher priority. Thus, the model without prioritization is more efficient in the use of raw material, while the model with prioritization offers greater agility to the production process. The choice of the most appropriate model should be guided by the respective context of each company, prioritizing cost or speed of production according to the operational needs of different situations.