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Single machine scheduling with total tardiness criterion and convex controllable processing times

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  • Kailiang Xu
  • Zuren Feng
  • Liangjun Ke

Abstract

We consider a single machine scheduling problem with total tardiness criteria and controllable job-processing times specified by a convex resource consumption function. The objective is to have the total tardiness limited into a given range, and minimize the total resource consumption. A polynomial time algorithm of O(n 2 ) is presented for the special case where jobs have a common due date. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Kailiang Xu & Zuren Feng & Liangjun Ke, 2011. "Single machine scheduling with total tardiness criterion and convex controllable processing times," Annals of Operations Research, Springer, vol. 186(1), pages 383-391, June.
    • Handle: RePEc:spr:annopr:v:186:y:2011:i:1:p:383-391:10.1007/s10479-010-0827-6
    DOI: 10.1007/s10479-010-0827-6
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    References listed on IDEAS

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    1. Jianzhong Du & Joseph Y.-T. Leung, 1990. "Minimizing Total Tardiness on One Machine is NP-Hard," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 483-495, August.
    2. Shabtay, Dvir & Kaspi, Moshe, 2006. "Parallel machine scheduling with a convex resource consumption function," European Journal of Operational Research, Elsevier, vol. 173(1), pages 92-107, August.
    3. Clyde L. Monma & Alexander Schrijver & Michael J. Todd & Victor K. Wei, 1990. "Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 736-748, November.
    4. Kailiang Xu & Zuren Feng & Liangjun Ke, 2010. "A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates," Annals of Operations Research, Springer, vol. 181(1), pages 303-324, December.
    5. R. G. Vickson, 1980. "Choosing the Job Sequence and Processing Times to Minimize Total Processing Plus Flow Cost on a Single Machine," Operations Research, INFORMS, vol. 28(5), pages 1155-1167, October.
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    Cited by:

    1. Carrasco, Rodrigo A. & Iyengar, Garud & Stein, Cliff, 2018. "Resource cost aware scheduling," European Journal of Operational Research, Elsevier, vol. 269(2), pages 621-632.
    2. Lin-Hui Sun & Kai Cui & Ju-Hong Chen & Jun Wang & Xian-Chen He, 2013. "Some results of the worst-case analysis for flow shop scheduling with a learning effect," Annals of Operations Research, Springer, vol. 211(1), pages 481-490, December.
    3. Lin-Hui Sun & Kai Cui & Ju-Hong Chen & Jun Wang & Xian-Chen He, 2013. "Research on permutation flow shop scheduling problems with general position-dependent learning effects," Annals of Operations Research, Springer, vol. 211(1), pages 473-480, December.

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