Minimizing the makespan on a single parallel batching machine

Authors:
Shenpeng Lu;Haodi Feng;Xiuqian Li
Affiliations:
School of Computer Science and Technology, Shandong University, China;School of Computer Science and Technology, Shandong University, China;School of Computer Science and Technology, Shandong University, China
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

In this paper, we consider the problem of scheduling with release dates and rejection on a single parallel batching machine, where the jobs have non-identical sizes. Our objective is to minimize the makespan of the accepted jobs plus the total penalty of the rejected jobs. First, we give a polynomial time approximation scheme (PTAS) for the case where jobs can be split. Then, we propose a 2-approximation algorithm for the special case with identical release dates. Finally, we present an approximation algorithm for the general problem with worst-case ratio 2+@e, where @e0 is an arbitrarily small constant.