Abstract
Abstract Cutting stock problems are within knapsack optimization problems and are considered as a non-deterministic polynomial-time (NP)-hard problem. In this paper, two-dimensional cutting stock problems were presented in which items and stocks were rectangular and cuttings were guillotine. First, a new, practical, rapid, and heuristic method was proposed for such problems. Then, the software implementation and architecture specifications were explained in order to solve guillotine cutting stock problems. This software was implemented by C++ language in a way that, while running the program, the operation report of all the functions was recorded and, at the end, the user had access to all the information related to cutting which included order, dimension and number of cutting pieces, dimension and number of waste pieces, and waste percentage. Finally, the proposed method was evaluated using examples and methods available in the literature. The results showed that the calculation speed of the proposed method was better than that of the other methods and, in some cases, it was much faster. Moreover, it was observed that increasing the size of problems did not cause a considerable increase in calculation time. In another section of the paper, the matter of selecting the appropriate size of sheets was investigated; this subject has been less considered by far. In the solved example, it was observed that incorrect selection from among the available options increased the amount of waste by more than four times. Therefore, it can be concluded that correct selection of stocks for a set of received orders plays a significant role in reducing waste.
Highlights
Cutting problems are derived from various industrial processes, for example, textile production systems, glass industries, steel, adhesive tape, wood, paper, etc. (Gonçalves 2007; Ben Messaoud et al 2008; Leung et al 2001; Erjavec et al 2009).The first research on cutting and packing problems was probably performed by Kantorovich in 1939 and Brooks in 1940, but extensive scientific work in this field began in 1960 as cited in Faina (1999), Dyckhoff (1990), and Javanshir and Shadalooee (2007)
Assumptions In this research, we make the following assumptions: a) Cuts are guillotine cuts. b)The stocks and items are rectangular. c) The orientation is fixed, and the items are not rotated. d)The assignment is of the third kind (Dyckhoff and Finke 1992; Wäscher et al 2007) because all items must be cut to serve all demands. e) The model is proposed under deterministic conditions. f ) The remaining sheets in each size, when all demands have been met, are considered as waste, they may be used for further orders. (Because the stocks are not assumed to be in rolls and are separated, if there are no orders left, the remaining parts of any size are considered temporarily as waste)
Suggested cutting approach As observed in Neapolitan and Naimipour (2004), packing and cutting stock problems are considered to be in the field of knapsack problems, which are non-deterministic polynomial-time (NP)-hard problems
Summary
The first research on cutting and packing problems was probably performed by Kantorovich in 1939 and Brooks in 1940, but extensive scientific work in this field began in 1960 as cited in Faina (1999), Dyckhoff (1990), and Javanshir and Shadalooee (2007). In 1990, Dyckhoff presented a systematic and consistent approach to the integration of different types of problems into a comprehensive typology based on the logical structure of cutting and packing problems. His goal was to assimilate the notations for various uses in the literature and to focus future research on specific types of problems (Dyckhoff 1990). There are several types of cutting problems based on different characteristics, which Dyckhoff divided into four groups based on their salient characteristics (dimension, type assignment, assortment of large objects, and small items) (Dyckhoff 1990; Dyckhoff and Finke 1992)
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