The unbounded parallel-batch scheduling with rejection

L Q Zhang, L F Lu and C T Ng
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L Q Zhang: Zhengzhou University, Zhengzhou, Henan, People's Republic of China
L F Lu: 1] Zhengzhou University, Zhengzhou, Henan, People's Republic of China[2] The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
C T Ng: The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Journal of the Operational Research Society, 2012, vol. 63, issue 3, 293-298

Abstract: In this paper, we consider the unbounded parallel-batch scheduling with rejection. A job is either rejected, in which case a certain penalty has to be paid, or accepted and processed in batches on a machine. The processing time of a batch is defined as the longest processing time of the jobs contained in it. Four problems are considered: (1) to minimize the sum of the total completion time of the accepted jobs and the total rejection penalty of the rejected jobs; (2) to minimize the total completion time of the accepted jobs subject to an upper bound on the total rejection penalty of the rejected jobs; (3) to minimize the total rejection penalty of the rejected jobs subject to an upper bound on the total completion time of the accepted jobs; (4) to find the set of all the Pareto optimal schedules. We provide a polynomial-time algorithm for the first problem. Furthermore, we show that all the other three problems are binary NP-hard and present a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for them.

Date: 2012
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