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Open AccessArticle

Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families

by Wenhua Li 1,*, Libo Wang 1, Xing Chai 2 and Hang Yuan 3
1
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
2
College of Science, Henan University of Technology, Zhengzhou 450001, China
3
Department of Economics, State University of New York at Binghamton, Binghamton, NY 13902, USA
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 170; https://doi.org/10.3390/math8020170
Received: 31 December 2019 / Revised: 22 January 2020 / Accepted: 24 January 2020 / Published: 1 February 2020
(This article belongs to the Special Issue Advances and Novel Approaches in Discrete Optimization)
We considered the online scheduling problem of simple linear deteriorating job families on m parallel batch machines to minimize the makespan, where the batch capacity is unbounded. In this paper, simple linear deteriorating jobs mean that the actual processing time p j of job J j is assumed to be a linear function of its starting time s j , i.e., p j = α j s j , where α j > 0 is the deterioration rate. Job families mean that one job must belong to some job family, and jobs of different families cannot be processed in the same batch. When m = 1 , we provide the best possible online algorithm with the competitive ratio of ( 1 + α max ) f , where f is the number of job families and α max is the maximum deterioration rate of all jobs. When m 1 and m = f , we provide the best possible online algorithm with the competitive ratio of 1 + α max .
Keywords: online algorithm; batch scheduling; linear deterioration; job families; competitive ratio online algorithm; batch scheduling; linear deterioration; job families; competitive ratio
MDPI and ACS Style

Li, W.; Wang, L.; Chai, X.; Yuan, H. Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families. Mathematics 2020, 8, 170.

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