Mathematical models for the minimization of open stacks problem

Autor(es)

Martin, Mateus ^[1] ; Yanasse, Horacio Hideki ^[1] ; Pinto, Maria Jose ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Paulo, Inst Ciencia & Tecnol, Ave Cesare Mansueto Giulio Lattes 1201, BR-12247014 Sao Jose Dos Campos, SP - Brazil

^[2] Inst Estudos Avancados IEAv, Div C4ISR, Trevo Coronel Aviador Jose Alberto Albano Amarant, BR-12228001 Sao Jose Dos Campos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: International Transactions in Operational Research; SEP 2021.
• Citações Web of Science: 0

Resumo

In this paper, we address the minimization of open stacks problem (MOSP). This problem often appears during production planning of manufacturing industries, such as in the cutting of objects to comply with space constraints around the cutting machine in the glass, furniture, and metallurgical industries. During the processing of the cutting patterns, all the copies of a demanded item are stored in a stack usually placed near the cutting machine. One stack for each type of demanded item, that is, different items do not share the same stack. In this sense, the MOSP consists of finding an optimal sequence of a given set of cutting patterns, while minimizing the maximum number of simultaneously open stacks. To effectively model and solve the problem, we present a novel integer linear programming (ILP) formulation based on a graph representation of the problem. We derive an ILP formulation from the modeling approach of Faggioli and Bentivoglio for the MOSP. Then we develop a simple constraint programming model based on interval variables and renewable resources. We performed computational experiments to evaluate the proposed approaches in comparison with other ILP formulations from the literature. Using a general-purpose solver, the proposed approaches perform well in terms of solution quality and computational time in comparison to the benchmark models for small and moderate-sized problem instances. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 20/00747-2 - Novas formulações para o problema de minimização de pilhas abertas e correlatos
• Beneficiário: Mateus Pereira Martin
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 16/01860-1 - Problemas de corte, empacotamento, dimensionamento de lotes, programação da produção, roteamento, localização e suas integrações em contextos industriais e logísticos
• Beneficiário: Reinaldo Morabito Neto
• Modalidade de apoio: Auxílio à Pesquisa - Temático