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Optimal on-line algorithms for one batch machine with grouped processing times

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Abstract

In this paper, we study on-line scheduling problems on a batch machine with the assumption that all jobs have their processing times in [p, (1+φ)p], where p>0 and \(\phi=(\sqrt{5}-1)/2\). Jobs arrive over time. First, we deal with the on-line problem on a bounded batch machine with the objective to minimize makespan. A class of algorithms with competitive ratio \((\sqrt{5}+1)/2\) are given. Then we consider the scheduling on an unbounded batch machine to minimize the time by which all jobs have been delivered, and provide a class of on-line algorithms with competitive ratio \((\sqrt{5}+1)/2\). The two class of algorithms are optimal for the problems studied here.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai, People’s Republic of China, 200237

    Yang Fang, Peihai Liu & Xiwen Lu

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  1. Yang Fang
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  2. Peihai Liu
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  3. Xiwen Lu
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Correspondence to Xiwen Lu.

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Fang, Y., Liu, P. & Lu, X. Optimal on-line algorithms for one batch machine with grouped processing times. J Comb Optim 22, 509–516 (2011). https://doi.org/10.1007/s10878-010-9298-6

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  • DOI: https://doi.org/10.1007/s10878-010-9298-6

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