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A MILP model for an extended version of the Flexible Job Shop Problem

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Abstract

A MILP model for an extended version of the Flexible Job Shop Scheduling problem is proposed. The extension allows the precedences between operations of a job to be given by an arbitrary directed acyclic graph rather than a linear order. The goal is the minimization of the makespan. Theoretical and practical advantages of the proposed model are discussed. Numerical experiments show the performance of a commercial exact solver when applied to the proposed model. The new model is also compared with a simple extension of the model described by Özgüven et al. (Appl Math Modell 34:1539–1548, 2010), using instances from the literature and instances inspired by real data from the printing industry.

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Acknowledgments

We thank Jun Zeng for several suggestions and discussions. This work was partially funded by CAPES, CNPq, FAPESP, and Hewlett-Packard GOLD advanced research grant, through HP Labs and HP Brazil.

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Authors and Affiliations

  1. Department of Computer Science, IME, University of São Paulo, São Paulo, Brazil

    Ernesto G. Birgin, Paulo Feofiloff, Cristina G. Fernandes & Marcio T. I. Oshiro

  2. Department of Production Engineering, EPUSP, University of São Paulo, São Paulo, Brazil

    Everton L. de Melo & Débora P. Ronconi

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  1. Ernesto G. Birgin
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  2. Paulo Feofiloff
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  3. Cristina G. Fernandes
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  4. Everton L. de Melo
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  5. Marcio T. I. Oshiro
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  6. Débora P. Ronconi
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Correspondence to Ernesto G. Birgin.

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Birgin, E.G., Feofiloff, P., Fernandes, C.G. et al. A MILP model for an extended version of the Flexible Job Shop Problem. Optim Lett 8, 1417–1431 (2014). https://doi.org/10.1007/s11590-013-0669-7

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  • DOI: https://doi.org/10.1007/s11590-013-0669-7

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