Abstract

Abstract
Cutting and packing problems are challenging combinatorial optimization problems that have many relevant industrial applications and arise whenever a raw material has to be cut into smaller parts while minimizing waste, or products have to be packed, minimizing the empty space. Thus, the optimal solution to these problems has a positive economic and environmental impact. In many practical applications, both the raw material and the cut parts have a rectangular shape, and cutting plans are generated for one raw material rectangle (also known as plate) at a time. This is known in the literature as the (two-dimensional) rectangular cutting problem. Many variants of this problem may arise, led by cutting technology constraints, raw-material characteristics, and different planning goals, the most relevant of which are the guillotine cuts. The absence of the guillotine cuts imposition makes the problem harder to solve to optimality. Based on the Floating-Cuts paradigm, a general and flexible mixed-integer programming model for the general rectangular cutting problem is proposed. To the best of our knowledge, it is the first mixed integer linear programming model in the literature for both non-guillotine and guillotine problems. The basic idea of this model is a tree search where branching occurs by successive first-order non-guillotine-type cuts. The exact position of the cuts is not fixed, but instead remains floating until a concrete small rectangle (also known as item) is assigned to a child node. This model does not include decision variables either for the position coordinates of the items or for the coordinates of the cuts. Under this framework, it was possible to address various different variants of the problem. Extensive computational experiments were run to evaluate the model's performance considering 16 different problem variants, and to compare it with the state-of-the-art formulations of each variant. The results confirm the power of this flexible model, as, for some variants, it outperforms the state-of-the-art approaches and, for the other variants, it presents results fairly close to the best approaches. But, even more importantly, this is a new way of looking at these problems which may trigger even better approaches, with the consequent economic and environmental benefits. © 2022 Elsevier Ltd

Abstract

Abstract
The CrossLog project aims to investigate, study, develop and implement an automated and collaborative cross-docking system (aligned with Industry 4.0) capable of moving and managing the flow of products within the warehouse in the fastest and safest way. In CrossLog, the ability to generate intelligent three-dimensional packing patterns is essential to ensure the flexibility and productivity of the cross-docking system while ensuring the stability of the palletised load. In this work, a heuristic solution approach is proposed to generate efficient pallet packing patterns that simultaneously minimise the total number of pallets required and address the balance of weight and volume between pallets. Computational experiments with data from a real company demonstrate the quality of the proposed solution approach.

Abstract
Over the years, methods and algorithms have been extensively studied to solve variations of the rectangular twodimensional strip packing problem (2D-SPP), in which small rectangles must be packed inside a larger object denominated as a strip, while minimizing the space necessary to pack all rectangles. In the rectangular 2D-SPP, constraints are used to restrict the packing process, satisfying physical and real-life practical conditions that can impact the material cutting. The objective of this paper is to present an extensive literature review covering scientific publications about the rectangular 2D-SPP constraints in order to provide a useful foundation to support new research works. A systematic literature review was conducted, and 223 articles were selected and analyzed. Real-life practical constraints concerning the rectangular 2D-SPP were classified into seven different groups. In addition, a bibliometric analysis of the rectangular 2D-SPP academic literature was developed. The most relevant authors, articles, and journals were discussed, and an analysis made concerning the basic constraints (orientation and guillotine cutting) and the main solving methods for the rectangular 2D-SPP. Overall, the present paper indicates opportunities to address real-life practical constraints.