Abstract
This paper is concerned with a semi-online scheduling problem with combined information on two identical parallel machines to minimize the makespan, where all the jobs have processing times in the interval \([1,\,t]\) \((t\ge 1)\) and the jobs arrive in non-increasing order of their processing times. The objective is to minimize the makespan. For \(t\ge 1\), we obtain a lower bound \(\max _{N=1,2,3,\ldots }\left\{ \min \{\frac{4N+3}{4N+2}\,,\frac{Nt+N+1}{2N+1}\}\right\} \) and show that the competitive ratio of the \(LS\) algorithm achieves the lower bound.
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Acknowledgments
We are grateful to the two anonymous referees for their thoughtful suggestions and comments which lead to the improvement of the paper. The first author is supported in part by NSF of China (61303010), and the second author is support in part by NSF of China (71125003), Specialized Research Fund for the Doctoral Program of Higher Education (20100073110024) and NCET-10-0578.
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Cao, Q., Wan, G. Semi-online scheduling with combined information on two identical machines in parallel. J Comb Optim 31, 686–695 (2016). https://doi.org/10.1007/s10878-014-9778-1
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DOI: https://doi.org/10.1007/s10878-014-9778-1