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Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach

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Abstract

In this study, we introduce a mixed nonlinear integer programming formulation for parallel machine earliness/tardiness (ET) scheduling with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we propose that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The model can easily provide the optimal solution to problems involving about eleven jobs and two machines.

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Authors and Affiliations

  1. Engineering Faculty, Industrial Engineering Department, Erciyes University, Kayseri, Turkey

    M. Duran Toksarı

  2. Engineering and Architecture Faculty, Industrial Engineering Department, Gazi University, Ankara, Turkey

    Ertan Güner

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  1. M. Duran Toksarı
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  2. Ertan Güner
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Correspondence to M. Duran Toksarı.

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Toksarı, M.D., Güner, E. Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach. Int J Adv Manuf Technol 38, 801–808 (2008). https://doi.org/10.1007/s00170-007-1128-3

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  • DOI: https://doi.org/10.1007/s00170-007-1128-3

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