A linear optimization approach to the combined production planning model

Gramani, Maria Cristina Nogueira; França, Paulo Morelato; Arenales, Marcos Nereu

doi:10.1016/j.jfranklin.2010.05.010

Cited by 38 publications

(22 citation statements)

References 24 publications

(25 reference statements)

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“…The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the wellknown lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem (Gramani et al, 2011). Kazemi Zanjani et al (2010) addressed a multi-period, multi-product sawmill production planning problem where the yields of processes were random variables because of nonhomogeneous quality of raw materials.…”

Section: Literature Reviewmentioning

confidence: 99%

A two-stage production planning model for perishable products under uncertainty

Jey¹,

Javanshir²,

Mohajeri³

2017

10.5267/j.uscm

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In this study, a multi-product, multi-period and non-linear programming model is developed for production planning problem where demand is under uncertainty. The proposed study is designed for a real-world case study of chemicals production factory with 1 production line and 2 manual and automatic technologies. In manual technology, workers are working with 3 amateur, typical and professional skills in 2 typical and overtime working. Automatic technology in this system has n machines in which the repairing and maintenance of the machineries are also included. This system has n products and the products are life-limited and with diversity. The primary goal is to propose a model for improvement of the production planning and minimization of the production system costs. The products in high volume and various types are produced and they are stored in bottles as the final products. For different production periods, the human forces capacities are considered and the level of employment or forces dismissal are considered. The production process is forwarding and backward process is not acceptable; that is, it is not allowable to rework in this system. Delivering final product from stockpiles to the retailers is conducted using vehicles with limited capacity. To solve the model in larger space and because of the complexity of the model, meta-heuristic algorithm is used. Finally, it is concluded that due to covering most of the assumptions in perishable products production, the proposed model is closer to the real-world circumstances and reduces costs in production systems.All rights reserved. Growing Science Ltd. 7

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Section: Literature Reviewmentioning

confidence: 99%

A two-stage production planning model for perishable products under uncertainty

Jey¹,

Javanshir²,

Mohajeri³

2017

10.5267/j.uscm

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“…However, the difficulty faced by this heuristic is that the resulting subproblems are N Phard capacitated lot-sizing problems. [28] relax setups for the problem but include the storage of parts in order to solve the problem more effectively. We also note the very recent work of [4] proposing robust models for coupled lot-sizing and cutting-stock in the furniture industry.…”

Section: Introductionmentioning

confidence: 99%

Progressive Selection Method for the Coupled Lot-Sizing and Cutting-Stock Problem

Akartunalı²,

Jans

et al. 2017

INFORMS Journal on Computing

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The coupled lot-sizing and cutting-stock problem has been a challenging and significant problem for industry, and has therefore received sustained research attention. The quality of the solution is a major determinant of cost performance in related production and inventory management systems, and therefore there is intense pressure to develop effective practical solutions. In the literature, a number of heuristics have been proposed for solving the problem. However, the heuristics are limited in obtaining high solution qualities. This paper proposes a new progressive selection algorithm that hybridizes heuristic search and extended reformulation into a single framework. The method has the advantage of generating a strong bound using the extended reformulation, which can provide good guidelines on partitioning and sampling in the heuristic search procedure so as to ensure an efficient solution process. We also analyze per-item and per-period Dantzig-Wolfe decompositions of the problem and present theoretical comparisons. The master problem of the per-period DantzigWolfe decomposition is often degenerate, which results in a tailing-off effect for column generation.We apply a hybridization of Lagrangian relaxation and stabilization techniques to improve the convergence. The discussion is followed by extensive computational tests, where we also perform detailed statistical analyses on various parameters. Comparisons with other methods indicate that our approach is computationally tractable and is able to obtain improved results.

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“…Alguns trabalhos correlatos, em que o problema de corte de estoque multiperíodo aparece como subproblema, envolvem o problema integrado de dimensionamento de lotes e corte de estoque. O problema integrado tem sido bastante estudado na literatura, por exemplo em: Gramani e França [5], Poltroniere et al [12], Gramani et al [6,7] e Silva et al [13].…”

Section: Introductionunclassified

O Problema de Corte de Estoque Bidimensional Multiperíodo

Poldi¹,

Araújo²

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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José do Rio Preto, SPResumo. O problema de corte de estoque multiperíodo surge imerso no planejamento e programação da produção em empresas que têm um estágio de produção caracterizado pelo corte de peças. As demandas dos itens ocorrem em períodos diversos de um horizonte de planejamento finito, sendo possível antecipar ou não a produção de itens. Os objetos disponíveis em estoque não utilizados em um período ficam disponíveis no próximo período, juntamente com novos objetos adquiridos ou produzidos pela própria empresa. Um modelo de otimização linear inteira de grande porte foi proposto na literatura para o caso unidimensional e o método simplex com geração de colunas foi especializado para resolver a relaxação linear do modelo proposto. Neste trabalho estendemos o modelo e o método para o caso bidimensional. Foram realizados experimentos computacionais que mostram que ganhos efetivos podem ser obtidos usando-se o modelo de corte de estoque multiperíodo, quando comparado com a solução lote-por-lote, tipicamente utilizada na prática.Palavras-chave. Problema de corte. Bidimensional. Multiperíodo. Programação linear. Geração de colunas. Grafo E/OU. IntroduçãoProblemas de corte de estoque consistem em cortar peças maiores (objetos) disponíveis em estoque com a finalidade de produzir peças menores (itens) para atender uma dada demanda, otimizando uma determinada função objetivo que pode ser, por exemplo, minimizar a perda de material ou o custo dos objetos cortados. Estes problemas são essenciais no planejamento da produção em muitas indústrias, tais como indústrias de papel, vidro, móveis, metalúrgica, plástica, têxtil etc [1].Com os avanços computacionais e também por motivos econômicos, as empresas têm se estimulado a tornar seus processos produtivos mais eficientes, o que induz, por sua vez, pesquisas acadêmicas de modelos de otimização para o controle e planejamento de sistemas produtivos.Neste contexto tem-se o problema de corte de estoque multiperíodo que consiste, basicamente, em resolver, a cada período em um horizonte de planejamento finito, um problema de corte de estoque, para atender a uma demanda de itens nos diversos períodos do 1

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A linear optimization approach to the combined production planning model

Cited by 38 publications

References 24 publications

A two-stage production planning model for perishable products under uncertainty

A two-stage production planning model for perishable products under uncertainty

Progressive Selection Method for the Coupled Lot-Sizing and Cutting-Stock Problem

O Problema de Corte de Estoque Bidimensional Multiperíodo

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