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Isomorphic scheduling problems

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  • Stanisław Gawiejnowicz
  • Alexander Kononov

Abstract

We consider general properties of isomorphic scheduling problems that constitute a new class of pairs of mutually related scheduling problems. Any such a pair is composed of a scheduling problem with fixed job processing times and its time-dependent counterpart with processing times that are proportional-linear functions of the job starting times. In order to introduce the class formally, first we formulate a generic scheduling problem with fixed job processing times and define isomorphic problems by a one-to-one transformation of instances of the generic problem into instances of time-dependent scheduling problems with proportional-linear job processing times. Next, we prove basic properties of isomorphic scheduling problems and show how to convert polynomial algorithms for scheduling problems with fixed job processing times into polynomial algorithms for proportional-linear counterparts of the original problems. Finally, we show how are related approximation algorithms for isomorphic problems. Applying the results, we establish new worst-case results for time-dependent parallel-machine scheduling problems and prove that many single- and dedicated-machine time-dependent scheduling problems with proportional-linear job processing times are polynomially solvable. Copyright Springer Science+Business Media, LLC 2014

Suggested Citation

  • Stanisław Gawiejnowicz & Alexander Kononov, 2014. "Isomorphic scheduling problems," Annals of Operations Research, Springer, vol. 213(1), pages 131-145, February.
    • Handle: RePEc:spr:annopr:v:213:y:2014:i:1:p:131-145:10.1007/s10479-012-1222-2
    DOI: 10.1007/s10479-012-1222-2
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    References listed on IDEAS

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    Cited by:

    1. Chen, Qianqian & Lin, Ling & Tan, Zhiyi & Yan, Yujie, 2017. "Coordination mechanisms for scheduling games with proportional deterioration," European Journal of Operational Research, Elsevier, vol. 263(2), pages 380-389.
    2. Gawiejnowicz, Stanisław & Kurc, Wiesław, 2015. "Structural properties of time-dependent scheduling problems with the lp norm objective," Omega, Elsevier, vol. 57(PB), pages 196-202.
    3. Rubing Chen & Jinjiang Yuan, 2020. "Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices," 4OR, Springer, vol. 18(2), pages 177-196, June.
    4. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    5. Sergey Kovalev, 2015. "Maximizing total tardiness on a single machine in $$O(n^2)$$ O ( n 2 ) time via a reduction to half-product minimization," Annals of Operations Research, Springer, vol. 235(1), pages 815-819, December.
    6. Wenhua Li & Libo Wang & Xing Chai & Hang Yuan, 2020. "Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families," Mathematics, MDPI, vol. 8(2), pages 1-12, February.

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