Scheduling resumable deteriorating jobs on a single machine with non-availability constraints

Authors:
Baoqiang Fan;Shisheng Li;Li Zhou;Liqi Zhang
Affiliations:
Department of Mathematics and Information, Ludong University, Yantai 264025, PR China and Department of Mathematics, Zhengzhou University, Zhengzhou 450001, PR China;Department of Mathematics, Zhengzhou University, Zhengzhou 450001, PR China;Department of Mathematics and Information, Ludong University, Yantai 264025, PR China;Department of Mathematics, Zhengzhou University, Zhengzhou 450001, PR China
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

We consider a problem of scheduling resumable deteriorating jobs on a single machine with non-availability constraints. The objective is to minimize the total completion time. We prove that the problem with a single non-availability period is NP-hard in the ordinary sense and possesses a fully polynomial-time approximation scheme. In addition, we show that there does not exist a polynomial-time approximation algorithm with a constant worst-case ratio for the problem with two or more non-availability periods, unless P=NP.