Production
https://prod.org.br/article/doi/10.1590/0103-6513.058512
Production
Article

Formulações matemáticas e estratégias de resolução para o problema job shop clássico

Mathematical models and resolution strategies for the classical job shop problem

Morales, Sergio Gomez; Ronconi, Debora Pretti

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Resumo

O problema de sequenciamento de tarefas no ambiente de produção job shop se caracteriza por conter n tarefas que devem ser processados por m máquinas, em que cada tarefa a ser realizada é constituída por um roteiro específico de operações com ordem de precedência preestabelecida. O objetivo deste trabalho é realizar uma análise comparativa das formulações matemáticas para este ambiente, minimizando o tempo total de execução de todas as tarefas em todas as máquinas (makespan). Modelos conhecidos e um novo modelo são avaliados e comparados através de testes computacionais em problemas-teste da literatura. Adicionalmente, estratégias de resolução são propostas. Experimentos computacionais utilizando um software comercial conhecido indicam que as estratégias propostas são eficientes para a redução do gap de otimalidade.

Palavras-chave

Job shop. Programação da produção, Makespan, Modelos de programação linear inteira mista.

Abstract

The scheduling problem in a job shop production environment is characterized by containing n jobs to be processed by m machines, where each job is represented by a specific sequence of operations with an established precedence order. The aim of this work is to perform a comparative analysis of the mathematical formulations for this environment by minimizing the makespan, i.e., the total time to complete all n jobs. Popular models and a proposed model are compared and evaluated through computational tests using cases from the literature. In addition, resolution strategies are proposed. Computational experiments using a well-known commercial software package indicate that the proposal strategies can promote a reduction of the optimality gap.

Keywords

Job shop, Scheduling, Makespan, Mixed integer linear programming models.

References

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