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Top1. Introduction
In general, companies have a strong desire to be more successful than others. They usually try to maximize their productivity while minimize their costs. The world is characterized by a rapid technological advancement; so that, companies invest in sophisticated machines and obtain new technologies. To maintain his competitivity, the company can focus and rely on some optimization techniques as tools of decision-making.
A regional industrial company in Tunisia fabricates foam mattresses and always complains about the high level of leftover resulting from cutting patterns choosing. These patterns are not predetermined through scientific approach but are developed manually based on the judgment and the experience of the employee. The principle goal of this study paper is to find a solution of the presented foam company and provide the final ordered items (mattress in foam) to customers.
We propose an optimization plan leads to generate efficient cutting patterns that will be able to minimize the current level of waste and therefore increase the satisfaction level of the owners. The final items (mattress in foam) made by guillotine cuts from bins (foam blocks), these bins in turn are made by tunnel. The bins of the same tunnel have the same weight and the same height but different lengths, so the objective is to minimize the total number of used bins (foam blocks) and therefore minimize the total length of tunnel (see Fig.1).
Figure 1.
Getting blocks from a tunnel
The treated problem represents one of the non-classical problems of the three dimensional (C&P) with additional constraints. Some constraints are solely determined by the industrial applications in (C&P) problem. This type of problem is important since it can help solve real industrial problems and minimize their costs. However, solving such practical problems is rather difficult because of the additional constraints encountered in the industry, such as the guillotine constraint presented in this paper. The considered problem presents specifications in the cutting process. Actually, the extraction of the final items (mattresses in foam) is made only by cuts from edge to edge. Indeed, literature defined this way of cut as guillotine cuts. These cuts are made by levels. The level is the number of phases necessary for the extraction of all the items. Fig.2. (a), (b), and (c).
Figure 2.
Example of cutting patterns. (a) Non-guillotine cuts. (b) 3-levels 2D guillotines cut. (c) 3-levels 3D guillotines cut.
Based on the last typology offered by Wäscher et al., (2007), the treated problem can be conceived as a variant of the three dimensional cutting stock problems when dimensions are not predetermined in advance (variable sizes). It is a strongly NP-hard problem, which cannot be easily solved in real cases. It has been less studied until very recently, even though it has a wide range of real applications.
Real problems can arise as a combination of several problems, including a range of specific technical constraints. This accentuated the difficulty of solving these problems. As such, the studied problem in this paper is a novel practical case belonging to the non-classical problems. It is an industrial foam-cutting problem that presents particular constraints linked, on the one hand, to the blocks production process using big Tunnels. On the other hand linked to the cutting ways, which follow the guillotine constraint. Solving such a type of problem in practical cases was and is still a big challenge.