Abstract
Cutting and packing problems are hard combinatorial optimization problems that arise in several manufacturing and process industries or in their supply chains. The solution of these problems is not only a scientific challenge but also has a large economic impact, as it contributes to the reduction of one of the major cost factors for many production sectors, namely raw materials, together with a positive environmental impact. The explicit consideration of uncertainty when solving cutting and packing problems with optimization techniques is crucial for a wider adoption of research results by companies. However, current research has paid little attention to the role of uncertainty in these problems. In this paper, we review the existing literature on uncertainty in cutting and packing problems, propose a classification framework, and highlight the many research gaps and opportunities for scientific contributions.

Abstract
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Abstract
This paper proposes a heuristic with stochastic neighborhood structures (SNS) to solve two-stage and three-stage two-dimensional guillotine bin packing and cutting stock problems. A solution is represented as a sequence of items which are packed into existing or new stacks, shelves or bins according to previously defined criteria. Moreover, SNS comprises three random neighborhood structures based on modifying the current sequence of items. These are called cut-and-paste, split, and swap blocks and are applied one by one in a fixed order to try to improve the quality of the current solution. Both benchmark instances and real-world instances provided by furniture companies were utilized in the computational tests. Particularly, all benchmark instances are bin packing instances (i.e., the demand of each item type is small), and all real-world instances are classified into bin packing instances and cutting stock instances (i.e., the demand of each item type is large). The computational results obtained by the proposed method are compared with lower bounds and with the solutions obtained by a deterministic Variable Neighborhood Descent (VND) meta-heuristic. The SNS provide solutions within a small percentage of the optimal values, and generally make significant improvements in cutting stock instances and slight to moderate improvements in bin packing instances over the VND approach.

Abstract
This article addresses several variants of the two-dimensional bin packing problem. In the most basic version of the problem it is intended to pack a given number of rectangular items with given sizes in rectangular bins in such a way that the number of bins used is minimized. Different heuristic approaches (greedy, local search, and variable neighbourhood descent) are proposed for solving four guillotine two-dimensional bin packing problems. The heuristics are based on the definition of a packing sequence for items and in a set of criteria for packing one item in a current partial solution. Several extensions are introduced to deal with issues pointed out by two furniture companies. Extensive computational results on instances from the literature and from the two furniture companies are reported and compared with optimal solutions, solutions from other five (meta) heuristics and, for a small set of instances, with the ones used in the companies.

Abstract
In this paper, an integer programming model for two-dimensional cutting stock problems is proposed. In the problems addressed, it is intended to cut a set of small rectangular items of given sizes from a set of larger rectangular plates in such a way that the total number of used plates is minimized. The two-stage and three-stage, exact and non-exact, problems are considered. Other issues are also addressed, as the rotation of items, the length of the cuts and the value of the remaining plates. The new integer programming model can be seen as an extension of the "one-cut model" proposed by Dyckhoff for the one-dimensional cutting stock problem. In the proposed model, each decision variable is associated with cutting one item from a plate or from a part of a plate resulting from previous cuts (residual plates). Comparative computational results of the proposed model and of models from the literature are presented and discussed.

Abstract