Minimizing the makespan on a single parallel batching machine

Lu, Shenpeng; Hu, Feng; Li, Xiuqian

doi:10.1016/j.tcs.2009.12.008

Cited by 8 publications

(1 citation statement)

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“…The preemptive cases are considered in [10] and [18]. The batch cases are studied in [4,[15][16][17]. Cao and Zhang [5] presented a PTAS for scheduling with rejection and job release times, which generalized the result in [3].…”

Section: Introductionmentioning

confidence: 99%

Parallel-Machine Scheduling Problem under the Job Rejection Constraint

Zhang

et al. 2014

Frontiers in Algorithmics

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Abstract. Given m identical machines and n independent jobs, each job Jj has a processing time (or size) pj and a penalty ej. A job can be either rejected, in which case its penalty is paid, or scheduled on one of the machines, in which case its processing time contributes to the load of that machine. The objective is to minimize the makespan of the schedule for accepted jobs under the constraint that the total penalty of the rejected jobs is no more than a given bound B. In this paper, we present a 2-approximation algorithm within strongly polynomial time and a polynomial time approximation scheme whose running time is O(nm2 ) for the general case. Moreover, we present a fully polynomial time approximation scheme for the case where the number of machines is a fixed constant. This result improves previous best running time from O(n m+2 / m ) to O(1/ 2m+3 + mn 2 ) .

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