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\iteman{io-port 05951383}
\itemau{Zhou, Weigang; Gao, Chengxiu; Huang, Kai}
\itemti{Parallel machine scheduling with controllable and simple linear increasing processing times.}
\itemso{Acta Math. Appl. Sin. 33, No. 4, 741-749 (2010).}
\itemab
Summary: This paper considers a parallel machine total weighted completion time scheduling problem with controllable and simple linear increasing processing times. We prove that for this NP-hard problem, there exists an optimal solution such that the processing time of each job is either fully reduced or not reduced at all, and for every machine, the optimal job sequence is defined by the increasing order of a certain function of the parameters and control decision of each job. By formulating the problem as a 0-1 nonlinear programming problem, we give a greedy algorithm for the scheduling problem.
\itemrv{~}
\itemcc{}
\itemut{parallel machine scheduling; processing time; 0-1 nonlinear programming; greedy algorithm}
\itemli{}
\end