![]() ![]() In this paper, problems in which both the small items and the large object are rectangles will be approached. The first two categories are self-explanatory and the last one refers to problems in which the small items have polygonal shapes, at least in the most common form of these problems. Two-dimensional problems are usually divided into rectangular, circular and irregular problems. Geometry also plays an important role in the description of small items' and large object's shapes. In this review two-dimensional SPP problems will be tackled. ![]() One should bear in mind that the dimensions that are common to the small items and the large object are not relevant for the optimization problem. However, for modeling and resolution purposes, C&P problems are usually classified in one-, two- and three-dimensional problems, when taking into account the number of dimensions that are relevant for the problem. When dealing with cutting of raw-material or item packing, three dimensions (length, width and height) are always present. One of the most distinctive characteristics of C&P problems is the fundamental role of geometry in their definition and resolution. The SPP can be found in many practical settings and has many real-world applications in industry and services, such as the cut of wood boards, steel plates or paper rolls and also multidimensional resource scheduling. Other well-known C&P problems are the knapsack problem, the bin-packing problem, the container loading problem, the cutting-stock problem and the pallet loading problem. European Journal of Operational Research, 183(3): 1109-1130.) typology for C&P problems. An improved typology of cutting and packing problems. This description fits the definition of a Cutting and Packing (C&P) problem and indeed the SPP can be classified as an Open Dimension Problem according to ( Wäscher et al., 2007 53 WÄSCHER G, HAUßNER H & SCHUMANN H. The small items cannot overlap each other and must be completely inside the large object. The Strip Packing Problem (SPP) aims to pack a set of small items inside a larger object, the container, with all dimensions but one fixed, with the objective of minimizing the free dimension of the large object. Two-dimensional rectangular strip packing problem cutting and packing heuristics Building on this review, research gaps are identified and the most interesting research directions pointed out. Both the seminal and the most recent approaches (from the last decade) will be reviewed, in a rather tutorial flavor, and classified according to their type: constructive heuristics, improvement heuristics with search over sequences and improvement heuristics with search over layouts. These problems have been intensively and extensively tackled in the literature and this paper will focus on heuristic resolution methods. a rectangle with a fixed width but an infinite height, being the problem's goal to place all rectangles on the strip so that the height is minimized. This survey approaches the specific C&P problem in which all items are rectangles, therefore fully characterized by a width and a height, and the large object is a strip, i.e. C&P problems differ from other combinatorial optimization problems by the intrinsic geometric constraints: items may not overlap and have to be fully contained in the large object. Two-dimensional rectangular strip packing problems belong to the broader class of Cutting and Packing (C&P) problems, in which small items are required to be cut from or packed on a larger object, so that the waste (unused regions of the large object) is minimized.
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