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The Scientific World Journal
Volume 2014 (2014), Article ID 270942, 7 pages
Research Article

Parallel Batch Scheduling of Deteriorating Jobs with Release Dates and Rejection

1School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China
2School of Management Sciences, Qufu Normal University, Rizhao, Shandong 276826, China

Received 12 March 2014; Accepted 1 July 2014; Published 21 July 2014

Academic Editor: Bahman Naderi

Copyright © 2014 Juan Zou and Cuixia Miao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the unbounded parallel batch scheduling with deterioration, release dates, and rejection. Each job is either accepted and processed on a single batching machine, or rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. First, we show that the problem is NP-hard in the ordinary sense. Then, we present two pseudopolynomial time algorithms and a fully polynomial-time approximation scheme to solve this problem. Furthermore, we provide an optimal time algorithm for the case where jobs have identical release dates.