Modeling and solving a real-world cutting stock problem in the marble industry via mathematical programming and stochastic diffusion search approaches

Baykasoğlu, Adil; Özbel, Burcu Kubur

doi:10.1016/j.cor.2020.105173

Cited by 14 publications

(7 citation statements)

References 54 publications

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“…Metasezgisel yöntemler, örnek alınan deney çalışmalarında her zaman kesin yöntemler kadar global iyi çözümler üretemese de başarılı sonuçlara ulaşılabileceği sonucuna varmışlardır [6]. Baykasog ve Özbel çalışmalarında, mermer blok kesme işlemi için geliştirdikleri matematiksel model ile metasezgisel yöntemi karşılaştırarak analiz etmişlerdir [7]. Saraç ve Sağır çalışmalarında, kesme problemi için tam sayılı matematiksel programlama modelleri kullanarak test problemlerini çözmüş ve elde edilen sonuçlarla karşılaştırma yapmışlardır [8].…”

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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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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“…Unlike other heuristic models, linear programming finds an optimal solution that satisfies an objective function [14], and interested parties can use linear programming to identify the alternative route that best achieves their objectives [15]. This type of model is applied in different contexts and to find optimal solutions with parameters that comprise a system, such as specific aspects associated to an activity of a production process, as in the case of [16], who proposes a mixed-integer linear programming (MILP) model to minimize waste in the current process of cutting marble slates, with the selection of marble blocks, taking into account the cutting sequence of the slate. Other studies have focused on logistics aspects, such as the minimization of transportation costs, such as the model proposed by [17], who proposes an optimal production distribution solution from 2 production sites to 9 distributors.…”

Section: State Of the Artmentioning

confidence: 99%

Linear Programming Model for Production Cost Minimization at a Rice Crop Products Manufacturer

Coronado-Hernández

Olarte-Jiménez

Herrera‐Fontalvo

et al. 2021

Communications in Computer and Information Science

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Companies in general must establish processes that generate profitability at lower costs. Manufacturing of rice crop protection products requires major investments and resource planning, including infrastructure, raw materials, technology, human resources, tests and trials, among others, which represents a major challenge. This paper proposes a methodology that aims to minimize production costs taking different factors into consideration. The first section identifies and describes the variables required for modeling. In the second section a linear programming model is formulated to determine the optimal function in terms of cost reduction. Lastly, the model was applied at a real company, producing satisfactory results in terms of an improved production plan and an 11% cost reduction, while enabling viewing the variables with greatest impact, such as storage and shift programming, with cost reductions of 68% and 44%, respectively. The purpose is to assist companies in this industry in applying mathematical programming models to solve problems and enable better resource planning to improve profitability.

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“…The single-period version of the problem was considered in Andrade et al (2014), where a discussion related to alternative definitions of usable leftovers was presented. Several papers in the literature, many of them based on real-world applications, address the one-dimensional cutting stock problem with usable leftovers; see the pioneers' works Roodman (1986); Scheithauer (1991) and the more recent works Cherri et al (2013Cherri et al ( , 2014; Poldi and Arenales (2010); Tomat and Gradišar (2017); Baykasoglu and Özbel (2021); Ali et al (2021); do Nascimento et al (2021). On the other hand, only a few publications tackle the two-dimensional case considered in the present work.…”

Section: Introductionmentioning

confidence: 99%

“…A relax-and-fix approach is proposed that solves the subproblems with a simplex method with column generation. Other recent works present practical applications in the marble industry (Baykasoglu and Özbel, 2021) and in the use of leftover piping in construction (Ali et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

The multiperiod two‐dimensional non‐guillotine cutting stock problem with usable leftovers

Birgin

Romão

Ronconi

2019

Int Trans Operational Res

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A mixed integer linear programing model for the two‐dimensional non‐guillotine cutting problem with usable leftovers was recently introduced by Andrade et al. The problem consists in cutting a set of ordered items using a set of objects of minimum cost and, within the set of solutions of minimum cost, maximizing the value of the usable leftovers. Since the concept of usable leftovers assumes they can potentially be used to attend new arriving orders, the problem is extended to the multiperiod framework in this work. In this way, the decision at each instant does not minimize in a myopic way the cost of the objects required to attend the orders of the current instant; but it aims to minimize the overall cost of the objects up to the considered time horizon. Some variants of the proposed model are analyzed and numerical results are presented.

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Modeling and solving a real-world cutting stock problem in the marble industry via mathematical programming and stochastic diffusion search approaches

Cited by 14 publications

References 54 publications

Bir Boyutlu Stok Kesme Probleminin Önerilen Sezgisel Algoritma Kullanılarak Çözümü

Bir Boyutlu Stok Kesme Probleminin Önerilen Sezgisel Algoritma Kullanılarak Çözümü

Linear Programming Model for Production Cost Minimization at a Rice Crop Products Manufacturer

The multiperiod two‐dimensional non‐guillotine cutting stock problem with usable leftovers

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