Bounded single-machine parallel-batch scheduling with release dates and rejection

Authors:
Lingfa Lu;T. C. E. Cheng;Jinjiang Yuan;Liqi Zhang
Affiliations:
Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China
Venue:
Computers and Operations Research
Year:
2009

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Abstract

We consider the bounded single-machine parallel-batch scheduling problem with release dates and rejection. A job is either rejected, in which case a certain penalty has to be paid, or accepted and then processed on the machine. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. When the jobs have identical release dates, we present a polynomial-time algorithm. When the jobs have a constant number of release dates, we give a pseudo-polynomial-time algorithm. For the general problem, we provide a 2-approximation algorithm and a polynomial-time approximation scheme.