Hybrid methods for lot sizing on parallel machines

Fiorotto, Diego Jacinto; Araújo, Silvio Alexandre de; Jans, Raf

doi:10.1016/j.cor.2015.04.015

Cited by 23 publications

(6 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Among the various extensions of the lot-sizing problem we highlight the use of several machines to produce the items ( Fiorotto & de Araujo, 2014;Fiorotto, de Araujo, & Jans, 2015;Jans, 2009;Toledo & Armentano, 2006 ), as well as the possibility of backlogging some part of the demand ( Gruson, Cordeau, & Jans, 2017;Pochet & Wolsey, 1988 ). The setup structure in the capacity constraint is another consideration that affects the problem complexity ( Karimi et al, 2003 ).…”

Section: Discussion Of the Lot-sizing Problemmentioning

confidence: 99%

“…These reformulations are strong formulations, since they provide tighter lower bounds when compared with the original formulations. Extensions of these reformulations have been successfully applied to obtain further improved lower bounds ( de Araujo & Clark, 2013;de Araujo, de Reyck, Degraeve, Fragkos, & Jans, 2015;Fiorotto et al, 2015;Jans & Degraeve, 2004;Süral, Denizel, & Wassenhove, 2009 ).…”

Section: Discussion Of the Lot-sizing Problemmentioning

confidence: 99%

See 1 more Smart Citation

Classification and literature review of integrated lot-sizing and cutting stock problems

Melega

Araújo

Jans

2018

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

a b s t r a c tThe aim of this paper is to classify the literature related to the integration between the lot-sizing and cutting stock problem. A deterministic mathematical model, that considers multiple dimensions of integration and comprises several aspects found in practice, is proposed. This model is used as a framework to classify the current literature in this field. The main classification of the literature is organized around two types of integration. In a planning horizon which consists of multiple periods, the inventory provides a link between the periods. This integration across time periods constitutes the first type of integration. The proposed model also considers the production of different types of items at three different levels: objects are fabricated or purchased and next cut into pieces which are then assembled into final products. The integration between these three production levels constitutes the second type of integration. The classification indicates that, even though many papers in the current literature analyze an integrated lot-sizing and cutting stock problem, they vary widely with respect to the level of integration on the time and production level dimensions. Furthermore, our analysis indicates that the current models also consider varying assumptions with respect to the inventory, the production capacities and the setups. Finally, we point out some possible interesting areas for future research. (R. Jans). that might correspond to customer requests, and a decision related to the cutting stock problem is needed. Part of the smaller reels can be cut again into paper sheets, according to some decision related to the lot size for the papers sheets. In the furniture industry, wooden plates are produced or purchased from different suppliers, and a decision about the size of the lots to be produced or purchased from each supplier must be taken. Then, these wooden plates are cut into several wooden parts (in a two-dimensional cutting stock process) to be assembled into the final products. A decision about the size of the lots of final products is also needed, and consequently there are three levels of decisions. Other examples can be found in the fiberglass industry, where fiberglass plates are cut to manufacture printed circuit boards and in the aluminium industry, where aluminium profiles are cut to make several window types. The basic idea of the integrated lot-sizing and cutting stock problem is to consider, simultaneously, the decisions related to both problems so as to capture the interdependency between these decisions in order to obtain a better global solution. Several papers from the literature present computational results showing the benefits of considering an integrated approach instead of taking decisions separately

show abstract

Section: Discussion Of the Lot-sizing Problemmentioning

confidence: 99%

Section: Discussion Of the Lot-sizing Problemmentioning

confidence: 99%

Classification and literature review of integrated lot-sizing and cutting stock problems

Melega

Araújo

Jans

2018

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…Fiorotto and de Araujo [13] applied a Lagrangian heuristic based on the relaxation of the demand constraints in order to find good feasible solutions. Fiorotto et al [14] proposed hybrid methods using Lagrangian relaxation and Dantzig-Wolfe decomposition and found better lower and upper bounds compared to Toledo and Armentano [47] and Fiorotto and de Araujo [13]. Recently, Vincent et al [49] developed a meta-heuristic based on the relaxation of the capacity constraints to explore the set of solutions and obtain more feasible solutions.…”

Section: Capacited Lot-sizing With Multiple Resourcesmentioning

confidence: 99%

“…There are several practical applications where parallel machines need to be taken into account, for example, the tire industry (Jans and Degraeve [22]), bottling of liquids (Carreno [8]) and pharmaceutical industry (Matta and Guignard [36]). In the standard design for lot sizing problems, each machine can manufacture all products, meaning the total or complete flexibility (Fiorotto et al [14], Toledo and Armentano [47]). However, it can be expensive to implement machines with total flexibility for several practical applications.…”

Section: Introductionmentioning

confidence: 99%

Evaluating process flexibility in lot sizing problems: an approach based on multicriteria decision making

et al. 2022

Self Cite

View full text Add to dashboard Cite

This paper presents a multicriteria analysis of the process flexibility in the context of the lot sizing problem with parallel machines. In the standard design for lot sizing problems, each machine can manufacture all products (total or complete flexibility). However, installing machines with complete flexibility for several practical applications can be costly. Therefore, it becomes interesting to implement only a limited amount of machine flexibility, where each machine can produce only a small number of different products. Recently, some works presented analyses of process flexibility by considering only the production cost as a criterion. However, the literature lacks a more comprehensive analysis that considers other essential criteria regarding the problem to compute the value of a flexibility configuration. Thus, we provide a detailed multicriteria analysis based on the TOPSIS method that produces a ranking of alternatives for the flexibility configurations. Extensive computational experiments and sensitivity analyses for different scenarios of the lot sizing problem compare individual flexibility configurations and evaluate its advantages in manufacturing planning. The computational results showed that limited flexibility configurations outperform the total flexibility in all scenarios. Moreover, different from the studies considering only the total cost as the criterion, investing in flexibility for all capacity levels has advantages.

show abstract

“…Na formulação clássica do problema de dimensionamento de lotes com máquinas paralelas [1], considera-se que cada máquina pode fabricar todos os produtos, essa configuração de flexibilidade é chamada flexibilidade total. Observe que quanto mais itens uma máquina puder fabricar (isso é, quanto mais flexível ela for), maior é o investimento necessário em tecnologia, desta forma, é preciso buscar configurações que sejam eficientes e econômicas.…”

unclassified

Estudo de Flexibilidade em problema de dimensionamento de lotes para sistemas não balanceados

Amaro¹,

Fiorotto²,

Oliveira³

2022

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

View full text Add to dashboard Cite

Resumo. Neste trabalho analisa-se os benefícios da flexibilidade de máquinas para o problema de dimensionamento de lotes não balanceado (número de itens maior do que o número de máquinas) em um contexto determinístico. Observa-se que diversos desafios se apresentam quando o sistema é não balanceado, como por exemplo, como construir/representar as configurações clássicas de flexibilidade. Nesse trabalho é proposto uma nova metodologia para se representar as configurações de flexibilidade através de uma abordagem utilizando conjuntos. Para analisar a metodologia desenvolvida, é proposto uma nova formulação matemática para o problema que considera o perfil da configuração de flexibilidade. Os resultados computacionais demonstram que mesmo quando a alocação dos itens às máquinas é realizada com a melhor configuração de flexibilidade, um dos benefícios da flexibilidade aparece como um impacto na redução do custo, e este impacto aumenta quando a alocação não é a melhor configuração.

show abstract

Hybrid methods for lot sizing on parallel machines

Cited by 23 publications

References 40 publications

Classification and literature review of integrated lot-sizing and cutting stock problems

Classification and literature review of integrated lot-sizing and cutting stock problems

Evaluating process flexibility in lot sizing problems: an approach based on multicriteria decision making

Estudo de Flexibilidade em problema de dimensionamento de lotes para sistemas não balanceados

Contact Info

Product

Resources

About