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An optimal online algorithm for two-machine open shop preemptive scheduling with bounded processing times

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Abstract

This paper deals with a two-machine open shop scheduling problem. The objective is to minimize the makespan. Jobs arrive over time. We study preemption-resume model, i.e., the currently processed job may be preempted at any moment in necessary and be resumed some time later. Let p 1, j and p 2, j denote the processing time of a job J j on the two machines M 1 and M 2, respectively. Bounded processing times mean that 1 ≤ p i, j ≤ α (i = 1, 2) for each job J j , where α ≥ 1 is a constant number. We propose an optimal online algorithm with a competitive ratio \({\frac{5\alpha-1}{4\alpha}}\) .

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References

  1. Borodin A., El-Yaniv R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  2. Pruhs, K., Sgall, J., Torng, E.: Online scheduling. In: Leung, J.Y.-T. (ed.) Handbook of Scheduling: Algorithms, Models, and Performance Analysis (2004)

  3. Vestjens, A.P.A.: On-line machine scheduling. PhD Thesis, Eindhoven University of Technology (1997)

  4. Chen B., Du D., Han J., Wen J.: On-line scheduling of small open shops. Discrete Appl. Math. 110, 133–150 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Pinedo M.: Scheduling: Theory, Algorithms, and Systems, 2nd edn. Prentice Hall, New York (2002)

    MATH  Google Scholar 

  6. Brucker P.: Scheduling Algorithms. Springer, Berlin (2007)

    MATH  Google Scholar 

  7. He Y., Zhang G.: Semi on-line scheduling on two identical machines. Computing 62, 179–187 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Angelelli E., Speranza M.G., Tuza Z.: Semi on-line scheduling on two parallel processors with upper bound on the items. Algorithmica 37, 243–262 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Angelelli E., Speranza M.G., Tuza Z.: New bounds and algorithms for on-line scheduling: two identical processors, known sum and upper bound on the tasks. Discrete Math. Theor. Comput. Sci. 8, 1–6 (2006)

    MATH  MathSciNet  Google Scholar 

  10. He Y., Dosa G.: Semi-online scheduling jobs with tightly-grouped processing times on three identical machines. Discrete Appl. Math. 150, 141–159 (2005)

    Article  MathSciNet  Google Scholar 

  11. Gonzalez T., Sahni S.: Open shop scheduling to minimize finish time. J. ACM 23, 665–679 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  12. Pardalos P., Shylo O.: An algorithm for the job scheduling problem based on global equilibrium techniques. Comput. Manag. Sci. 3, 331–348 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Pardalos, P., Shylo, O., Vazacopoulos, A.: Solving job shop scheduling problems utilizing the properties of backbone and “big valley”. Comput. Optim. Appl. doi:10.1007/s10589-008-9206-5

  14. Rocha P., Ravetti M., Mateus G., Pardalos P.: Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput. Oper. Res. 35, 1250–1264 (2008)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Management, Xi’an Jiaotong University, 710049, Xi’an, Shaanxi, People’s Republic of China

    Ming Liu, Chengbin Chu, Yinfeng Xu & Feifeng Zheng

  2. Laboratoire Génie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92295, Châtenay-Malabry Cedex, France

    Ming Liu & Chengbin Chu

  3. State Key Laboratory for Manufacturing Systems Engineering, 710049, Xi’an, Shaanxi, People’s Republic of China

    Yinfeng Xu & Feifeng Zheng

Authors
  1. Ming Liu
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  2. Chengbin Chu
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  3. Yinfeng Xu
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  4. Feifeng Zheng
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Correspondence to Ming Liu.

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Liu, M., Chu, C., Xu, Y. et al. An optimal online algorithm for two-machine open shop preemptive scheduling with bounded processing times. Optim Lett 4, 227–237 (2010). https://doi.org/10.1007/s11590-009-0163-4

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  • DOI: https://doi.org/10.1007/s11590-009-0163-4

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