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A note on minimizing the sum of squares of machine completion times on two identical parallel machines

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  • Rico Walter

    (Fraunhofer Institute for Industrial Mathematics ITWM)

Abstract

In this short note, we address the coherence between minimizing the sum of squares of machine completion times and minimizing makespan on two identical parallel machines. We show equivalence of the two objectives and identify interesting and useful relations which allow us to transfer worst-case ratios of approximation algorithms from one problem to the other.

Suggested Citation

  • Rico Walter, 2017. "A note on minimizing the sum of squares of machine completion times on two identical parallel machines," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(1), pages 139-144, March.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:1:d:10.1007_s10100-015-0429-0
    DOI: 10.1007/s10100-015-0429-0
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    References listed on IDEAS

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    1. Koulamas, Christos & Kyparisis, George J., 2008. "An improved delayed-start LPT algorithm for a partition problem on two identical parallel machines," European Journal of Operational Research, Elsevier, vol. 187(2), pages 660-666, June.
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    Cited by:

    1. Federico Della Croce & Rosario Scatamacchia & Vincent T’kindt, 2019. "A tight linear time $$\frac{13}{12}$$ 13 12 -approximation algorithm for the $$P2 || C_{\max }$$ P 2 | | C max problem," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 608-617, August.
    2. Bentao Su & Naiming Xie, 2020. "Single workgroup scheduling problem with variable processing personnel," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 671-684, June.

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