摘要
In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' of the job on position i and a “normal' processing time of the job. The criteria considered is to minimize scheduled length of all jobs. A lemma is proposed and proved. In no deadline constrained condition, the problem belongs to polynomial time algorithm. It is proved by using 3 partition that if the problem is deadline constrained, its complexity is strong NP hard. Finally, a conjuncture is proposed that is to be proved.
In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' of the job on position i and a “normal' processing time of the job. The criteria considered is to minimize scheduled length of all jobs. A lemma is proposed and proved. In no deadline constrained condition, the problem belongs to polynomial time algorithm. It is proved by using 3 partition that if the problem is deadline constrained, its complexity is strong NP hard. Finally, a conjuncture is proposed that is to be proved.
