An efficient mathematical model for solving one-dimensional cutting stock problem using sustainable trim

Vishwakarma, Ravi; Powar, P. L.

doi:10.1016/j.aime.2021.100046

Cited by 4 publications

(4 citation statements)

References 37 publications

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“…The results confirm that combining stocks with special lengths reduces the waste rate than combination by stock length. In Vishwakarma & Powar (2021) a mathematical model is presented, where a sustainable trim is defined as a trim loss that has a less negative economic impact on the company. The sustainable trim is used as an upper bound for all cutting patterns.…”

Section: State Of the Art Of 1d-cspmentioning

confidence: 99%

Minimizing the total waste in the one-dimensional cutting stock problem with the African buffalo optimization algorithm

Montiel-Arrieta,

Barragan-Vite,

Seck-Tuoh-Mora

et al. 2023

PeerJ Computer Science

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The one-dimensional cutting-stock problem (1D-CSP) consists of obtaining a set of items of different lengths from stocks of one or different lengths, where the minimization of waste is one of the main objectives to be achieved. This problem arises in several industries like wood, glass, and paper, among others similar. Different approaches have been designed to deal with this problem ranging from exact algorithms to hybrid methods of heuristics or metaheuristics. The African Buffalo Optimization (ABO) algorithm is used in this work to address the 1D-CSP. This algorithm has been recently introduced to solve combinatorial problems such as travel salesman and bin packing problems. A procedure was designed to improve the search by taking advantage of the location of the buffaloes just before it is needed to restart the herd, with the aim of not to losing the advance reached in the search. Different instances from the literature were used to test the algorithm. The results show that the developed method is competitive in waste minimization against other heuristics, metaheuristics, and hybrid approaches.

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Section: State Of the Art Of 1d-cspmentioning

confidence: 99%

Minimizing the total waste in the one-dimensional cutting stock problem with the African buffalo optimization algorithm

Montiel-Arrieta,

Barragan-Vite,

Seck-Tuoh-Mora

et al. 2023

PeerJ Computer Science

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“…Vishwakarma ve Powar çalışmalarında, bir boyutlu stok kesme problemini incelemişlerdir. Kesme kaybını en aza indirecek kesme planı oluşturmak için matematiksel ve metasezgisel yöntemleri kullanmışlardır [14]. Parreno ve Alvarez-Valdes'in çalışmalarında, giotin kullanılarak yapılan iki boyutlu stok kesme problemini, geliştirdikleri tam sayılı doğrusal programlamayla çözmüşlerdir [15].…”

Section: Literatür Taramasıunclassified

Bir Boyutlu Stok Kesme Probleminin Önerilen Sezgisel Algoritma Kullanılarak Çözümü

TOPAL,

KUMRU

2023

Kocaeli Üniversitesi Fen Bilimleri Dergisi

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Bu çalışmada, bir boyutlu stok kesme problemi üzerinde çalışılmıştır. Kesme işlemi sayısının fazla olması bir boyutlu kesme probleminin çözümünde hesaplama zorluklarını ortaya çıkarmaktadır. Kesme işlemlerinin yoğun yapıldığı ve hesaplama zorluklarının yaşandığı bir tesiste daha verimli bir kesme işlemi sağlanması hedeflenmiştir. Bu tesiste metal kesme işlemleri referans alınmış ve test verileri hazırlanarak farklı yöntemler aracılığıyla problemler çözülmüştür. Ele alınan kesme problemi için geliştirilen sezgisel algoritma, tavlama benzetimi, tam sayılı matematiksel programlama ve Real Cut 1D hazır paket programıyla çözümler karşılaştırılmıştır. Sonuçlar sarf edilen ana malzeme, fire oranları ve çözüm süreleri açısından değerlendirilmiştir. Kullanılan yöntemlerin sarf edilen ana malzeme ve fire oranı bakımından yüksek verimliliğe sahip oldukları görülmüştür. Hesaplama süresi açısından bakıldığında geliştirilen sezgisel algoritma ve Real Cut 1D programı diğer yöntemlere göre daha iyi sonuçlar ürettiği tespit edilmiştir. Geliştirilen sezgisel algoritma çözüm, fire oranı ve hesaplama süresi açısından gayet iyi sonuçlar üretmesi nedeniyle tercih edilebilir yöntemlerden biri olabileceği sonucuna ulaşılmıştır.

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“…They then offered two models based on the pattern for 2DCSP (Gilmore & Gomory, 1965). The problem for 1DCSP has been discussed in many models and algorithms, such as linear programming based heuristic algorithm based on full pattern model (Alvarez-Valdes et al, 2002) using dynamic programming for procedure column generation and heuristic column generation based on GRASP (Greedy Randomizes Adaptive Search Procedure) and Tabu Search (Beasley, 1985); the use of the arc-flow model for one-dimensional bin packing problems (Valério de Carvalho, 2002); modification of the branch and bound algorithm (N. Rodrigo et al, 2015); the least loser for the Bi-objective (Alfares & Alsawafy, 2019); meraheuristics for one dimension (Ravelo et al, 2020); the greedy heuristic that governs (Cerqueira et al, 2021); pattern-set creation algorithm for a stock problem with cost setup (Cui et al, 2015); the arc flow and one-cut models can be used for one-dimensional CSP problems (Martinovic et al, 2018); a mathematical model to solve the one-dimensional stock reduction problem using continuous trim by comparing the Residual Greedy Rounding (RGR) and CUT models (Vishwakarma & Powar, 2021). Then for the one-dimensional two-stage CSP, there are several proposed methods to determine the solution, namely the first method based on intelligent enumeration of intermediaries using the dominance relation specified for the backpack problem, the second method with the branch and bound algorithm, and the third method is a hybrid algorithm (Muter & Sezer, 2018).…”

Section: A Introductionmentioning

confidence: 99%

Pattern Generation for Three Dimensional Cutting Stock Problem

Atika

Silalahi

Bukhari

2022

JTAM

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We consider the problem of three-dimensional cutting of a large block that is to be cut into some small block pieces, each with a specific size and request. Pattern generation is an algorithm that has been used to determine cutting patterns in one-dimensional and two-dimensional problems. The purpose of this study is to modify the pattern generation algorithm so that it can be used in three-dimensional problems, and can determine the cutting pattern with the minimum possible cutting residue. The large block will be cut based on the length, width, and height. The rest of the cuts will be cut back if possible to minimize the rest. For three-dimensional problems, we consider the variant in which orthogonal rotation is allowed. By allowing the remainder of the initial cut to be rotated, the dimensions will have six permutations. The result of the calculation using the pattern generation algorithm for three-dimensional problems is that all possible cutting patterns are obtained but there are repetitive patterns because they suggest the same number of cuts.

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An efficient mathematical model for solving one-dimensional cutting stock problem using sustainable trim

Cited by 4 publications

References 37 publications

Minimizing the total waste in the one-dimensional cutting stock problem with the African buffalo optimization algorithm

Minimizing the total waste in the one-dimensional cutting stock problem with the African buffalo optimization algorithm

Bir Boyutlu Stok Kesme Probleminin Önerilen Sezgisel Algoritma Kullanılarak Çözümü

Pattern Generation for Three Dimensional Cutting Stock Problem

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