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Single machine scheduling with sum-of-logarithm-processing-times based and position based learning effects

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Abstract

In this paper we consider the single machine scheduling problems with sum-of-logarithm-processing-times based and position based learning effects, i.e., the actual job processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in a sequence. The logarithm function is used to model the phenomenon that learning as a human activity is subject to the law of diminishing return. We show that even with the introduction of the proposed model to job processing times, several single machine problems remain polynomially solvable.

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References

  1. Badiru A.B.: Computational survey of univariate and multivariate learning curve models. IEEE Trans. Eng. Manag. 39, 176–188 (1992)

    Article  Google Scholar 

  2. Biskup D.: Single-machine scheduling with learning considerations. Eur. J. Oper. Res. 115, 173–178 (1999)

    Article  MATH  Google Scholar 

  3. Biskup D.: A state-of-the-art review on scheduling with learning effects. Eur. J. Oper. Res. 188, 315–329 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cheng T.C.E., Wang G.: Single machine scheduling with learning effect considerations. Ann. Oper. Res. 98, 273–290 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cheng T.C.E., Wu C.-C., Lee W.-C.: Some scheduling problems with deteriorating jobs and learning effects. Comput. Ind. Eng. 54, 972–982 (2008)

    Article  Google Scholar 

  6. Cheng T.C.E., Wu C.-C., Lee W.-C.: Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects. Inf. Sci. 178, 2476–2487 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cheng T.C.E., Lai P.-J., Wu C.-C., Lee W.-C.: Single-machine scheduling with sum-of-logarithm-processing-times-based learning considerations. Inf. Sci. 179, 3127–3135 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cheng T.C.E., Wu C.-C., Lee W.-C.: Scheduling problems with deteriorating jobs and learning effects including proportional setup times. Comput. Ind. Eng. 58, 326–331 (2010)

    Article  Google Scholar 

  9. Graham R.L., Lawler E.L., Lenstra J.K., Rinnooy Kan A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5, 287–326 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  10. Huang X., Wang J.-B., Wang L.-Y., Gao W.-J., Wang X.-R.: Single machine scheduling with time-dependent deterioration and exponential learning effect. Comput. Ind. Eng. 58, 58–63 (2010)

    Article  Google Scholar 

  11. Huang X., Wang M.-Z., Wang J.-B.: Single machine group scheduling with both learning effects and deteriorating jobs. Comput. Ind. Eng. 60, 750–754 (2011)

    Article  Google Scholar 

  12. Lee W.-C., Wu C.-C.: Some single-machine and m-machine flowshop scheduling problems with learning considerations. Inf. Sci. 179, 3885–3892 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lee W.-C., Wu C.-C.: A note on single-machine group scheduling problems with position-based learning effect. Appl. Math. Model. 33, 2159–2163 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mosheiov G.: Minimizing total absolute deviation of job completion times: extensions to position-dependent processing times and parallel identical machines. J. Oper. Res. Soc. 59, 1422–1424 (2008)

    Article  MATH  Google Scholar 

  15. Pinedo M.: Scheduling: theory, algorithms, and systems. Prentice-Hall, Upper Saddle River (2002)

    Google Scholar 

  16. Townsend W.: The single machine problem with quadratic penalty function of completion times: a branch-and-bound solution. Manag. Sci. 24, 530–534 (1978)

    Article  MATH  Google Scholar 

  17. Wang J.-B.: Single-machine scheduling with past-sequence-dependent setup times and time-dependent learning effect. Comput. Ind. Eng. 55, 584–591 (2008)

    Article  Google Scholar 

  18. Wang J.-B.: Single-machine scheduling with a sum-of-actual-processing-time based learning effect. J. Oper. Res. Soc. 61, 172–177 (2010)

    Article  MATH  Google Scholar 

  19. Wang J.-B., Ng C.T., Cheng T.C.E., Liu L.L.: Single-machine scheduling with a time-dependent learning effect. Int. J. Prod. Econ. 111, 802–811 (2008)

    Article  Google Scholar 

  20. Wang J.-B., Wang D., Wang L.-Y., Lin L., Yin N., Wang W.-W.: Single machine scheduling with exponential time-dependent learning effect and past-sequence-dependent setup times. Comput. Math. Appl. 57, 9–16 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Wang J.-B., Wang M.-Z.: Single machine multiple common due dates scheduling with general job-dependent learning curves. Comput. Math. Appl. 60, 2998–3002 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  22. Wang J.-B., Wang M.-Z.: A revision of machine scheduling problems with a general learning effect. Math. Comput. Model. 53, 330–336 (2011)

    Article  MATH  Google Scholar 

  23. Wang J.-B., Li J.-X.: Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects. Appl. Math. Model. 35, 1388–1395 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  24. Wright T.P.: Factors affecting the cost of airplanes. J. Aeronaut. Sci. 3, 122–128 (1936)

    Article  Google Scholar 

  25. Wu C.C., Lee W.C.: Single-machine and flowshop scheduling with a general learning effect model. Comput. Ind. Eng. 56, 1553–1558 (2009)

    Article  Google Scholar 

  26. Yang D.-L., Kuo W.-H.: Single-machine scheduling with both deterioration and learning effects. Ann. Oper. Res. 172, 315–327 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  27. Yang D.-L., Kuo W.-H.: Some scheduling problems with deteriorating jobs and learning effects. Comput. Ind. Eng. 58, 25–28 (2010)

    Article  Google Scholar 

  28. Yin Y., Xu D., Sun K., Li H.: Some scheduling problems with general position-dependent and time-dependent learning effects. Inf. Sci. 179, 2416–2425 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  29. Zhang, X., Yan, G., Zhang, F., Tang, G.: Machine scheduling algorithm with a new learning effect. J. Syst. Sci. Math. Sci. 30, 1359–1367 (2010, in Chinese)

    Google Scholar 

Download references

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Authors and Affiliations

  1. School of Science, Shenyang Aerospace University, Shenyang, 110136, China

    Ji-Bo Wang

  2. Faculty of Management and Economics, Dalian University of Technology, Dalian, 116024, China

    Jian-Jun Wang

Authors
  1. Ji-Bo Wang
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  2. Jian-Jun Wang
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Correspondence to Ji-Bo Wang.

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Wang, JB., Wang, JJ. Single machine scheduling with sum-of-logarithm-processing-times based and position based learning effects. Optim Lett 8, 971–982 (2014). https://doi.org/10.1007/s11590-012-0494-4

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  • DOI: https://doi.org/10.1007/s11590-012-0494-4

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