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Dynamic Scheduling on a Single Batch Processing Machine with Split Compatibility Graphs

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Journal of Mathematical Modelling and Algorithms

Abstract

We consider the problem of minimizing the makespan on a batch processing machine, in which jobs are not all compatible. Only compatible jobs can be included into the same batch. This relation of compatibility is represented by a split graph. Jobs have release dates. The capacity of the batch processing machine is finite or infinite. The processing time of a batch is given by the processing time of the longest job in the batch. We establish the NP-hardness of the general problem and present polynomial algorithms for several special cases. Relating scheduling theory and graph theory appears to be an interesting and important concept.

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Authors and Affiliations

  1. Institut de Mathématiques, Université USTHB, BP 32, Bab-Ezzouar, El-Alia, 16111, Alger, Algeria

    Mourad Boudhar

  2. Laboratoire Leibniz, Institut IMAG, 46 avenue Felix Viallet, 38031, Grenoble, France

    Mourad Boudhar

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  1. Mourad Boudhar
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Boudhar, M. Dynamic Scheduling on a Single Batch Processing Machine with Split Compatibility Graphs. Journal of Mathematical Modelling and Algorithms 2, 17–35 (2003). https://doi.org/10.1023/A:1023669107449

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  • DOI: https://doi.org/10.1023/A:1023669107449

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