Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization

Abstract

In the two‐dimensional (2D) cutting (2DC) problem, a large rectangular sheet has to be dissected into smaller rectangular pieces with the aim of maximizing the total profit associated with the extracted pieces. When the number of copies of each piece to be extracted is bounded, it is referred to as constrained 2DC (C2DC) problem. The C2DC has been widely studied by the operations research community for its applications and theoretical issues. In this work, we recall the best exact and heuristic solving approaches for the C2DC and we provide a review and a categorization of the available upper bounds. We also discuss improvements and combinations of these upper bounds and give directions for their effective exploitation. Finally, we demonstrate the loss of accuracy of several exact methods present in literature because of the effect of the used antiredundancy strategies on the implemented bounding criteria. This work, based on more than 90 contributions, has a twofold target. For researchers working in C2DC, it provides a useful insight on the topic. For expert practitioners, it represents a systematic collection of the main findings and achievements, posing also the basis for future research.

2DPackLib: a two-dimensional cutting and packing library

“…In the following decade, a survey on general two-dimensional packing problems was proposed by Alvarez-Valdes et al [1]. Surveys on specific problems, variants, and methodologies were produced by Lodi et al [30] (2D-BPP and 2D-SPP), Silva et al [44] (pallet loading problem, a variant of the 2D-BPP in which one has to pack, with orthogonal rotations, the maximum number of identical items into a single bin), Oliveira et al [40] (2D-SPP), Christensen et al [14] (approximation and online algorithms), and Russo et al [41] (upper bounds for problems with guillotine cuts).…”

A cutting stock problem in the wood products industry: a two‐stage solution approach

“…The literature review is limited to the mathematical modeling and analysis. Our research also falls within the field of heuristic and metaheuristic (e.g., Stadtler, 1990;Lai and Chan, 1997;Hifi and Roucairol, 2001); interested readers can be referred to the recent papers by Sanchez et al (2018), Russo et al (2020), and the references therein. In Table 1, a literature summary is provided to reveal the research gaps in the literature.…”

Research on Fish Slicing Method Based on Simulated Annealing Algorithm

“…In many industries, the cut size and type of expected products are fixed, and it is necessary to optimize the arrangement and combination of cutting methods for raw materials of different sizes. In many industries (such as paper, cloth, metal plates, and wood), there are multiobjective cutting optimization problems, all of which aim to obtain small products that meet customer needs from large raw materials under the conditions of meeting multiple optimization objectives [7,8]. For example, in the textile industry, the fabric cutting position needs to be determined according to customer quality requirements.…”