Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines

Autor(es)

Fiorotto, Diego Jacinto ^[1] ; de Araujo, Silvio Alexandre ^[1]

Afiliação do(s) autor(es)

^[1] UNESP Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ANNALS OF OPERATIONS RESEARCH; v. 217, n. 1, p. 213-231, JUN 2014.
• Citações Web of Science: 10

Resumo

We consider the capacitated lot sizing problem with multiple items, setup time and unrelated parallel machines. The aim of the article is to develop a Lagrangian heuristic to obtain good solutions to this problem and good lower bounds to certify the quality of solutions. Based on a strong reformulation of the problem as a shortest path problem, the Lagrangian relaxation is applied to the demand constraints (flow constraint) and the relaxed problem is decomposed per period and per machine. The subgradient optimization method is used to update the Lagrangian multipliers. A primal heuristic, based on transfers of production, is designed to generate feasible solutions (upper bounds). Computational results using data from the literature are presented and show that our method is efficient, produces lower bounds of good quality and competitive upper bounds, when compared with the bounds produced by another method from the literature and by high-performance MIP software. (AU)

• Processo FAPESP: 11/22647-0 - Problemas de dimensionamento de lotes: integrações e métodos de solução
• Beneficiário: Silvio Alexandre de Araujo
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 10/16727-9 - Relaxação lagrangiana e decomposição dantzig-wolfe: aplicação ao problema de dimensionamento de lotes em máquinas paralelas
• Beneficiário: Diego Jacinto Fiorotto
• Modalidade de apoio: Bolsas no Brasil - Doutorado