Minimizing the maximum lateness on a two machine flowshop with batch processors

Minimizing the maximum lateness on a two machine flowshop with batch processors

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Article ID: iaor20053104
Country: China
Volume: 22
Issue: 2
Start Page Number: 247
End Page Number: 251
Publication Date: Jun 2004
Journal: Journal of Applied Sciences
Authors: , , ,
Keywords: flowshop
Abstract:

This paper considers the following problem: n jobs need to be processed on two machines (M1, M2) successively. The deadline for job j is dj, and the processing times of job j on M1, M2 are aj,bj respectively. Both machines are batch processors. This means n jobs are grouped into several batches on Mi, i = 1,2, respectively, and the machines process the jobs in same batch simultaneously. The processing time of a batch is equal to the longest processing time for all the jobs in this batch. Thus all the jobs in same batch are processed in the same length of time on the given machine, and the jobs will also be shifted in batches. We take the maximum lateness as our objective function for minimization. After pointing out that this scheduling problem is NP-hard, we give some special cases that can be solved in polynomial time and construct the corresponding dynamic programming.

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