Dynamic Scheduling on a Single Batch Processing Machine with Split Compatibility Graphs |
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Authors: | Mourad Boudhar |
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Affiliation: | (1) Institut de Mathématiques, Université USTHB, BP 32, Bab-Ezzouar, El-Alia, 16111, Alger, Algeria;(2) Laboratoire Leibniz, Institut IMAG, 46 avenue Felix Viallet, 38031 Grenoble, France |
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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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Keywords: | batch processing machine batch scheduling compatibility graph split graph |
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