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Single-machine scheduling with accelerating deterioration effects

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Abstract

Scheduling with deterioration effects has been widely investigated in the past two decades. In realistic situations, the deterioration effect might accelerate, especially in the food manufacturing industry. In this paper we propose a scheduling model with an accelerating deterioration effect. We show that the single-machine problems under the model to minimize the makespan, total completion time, total weighted completion time, maximum lateness, maximum tardiness, and total tardiness remain polynomially solvable.

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References

  1. Alidaee B., Womer N.K.: Scheduling with time dependent processing times: review and extensions. J. Oper. Res. Soc. 50, 711–720 (1999)

    MATH  Google Scholar 

  2. Bank, M., Fatemi Ghomi, S.M.T., Jolai, F., Behnamian, J.: Two-machine flow shop total tardiness scheduling problem with deteriorating jobs. Appl. Math. Model. doi:10.1016/j.apm.2011.12.010 (2012)

  3. Brancato E.: Life expectancy of motors. IEEE Electr. Insul. Mag. 7(6), 14–22 (1991)

    Article  Google Scholar 

  4. Browne S., Yechiali U.: Scheduling deteriorating jobs on a single processor. Oper. Res. 38(3), 495–498 (1990)

    Article  MATH  Google Scholar 

  5. Chan F.T.S., Lau H.C.W., Ip R.W.L., Chan H.K., Kong S.: Implementation of total productive maintenance: a case study. Int. J. Prod. Econ. 95(1), 71–94 (2005)

    Article  Google Scholar 

  6. Cheng T.C.E., Ding Q., Lin B.M.T.: A concise survey of scheduling with time-dependent processing times. Eur. J. Oper. Res. 152, 1–13 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cheng T.C.E., Hsu C.J., Huang Y.C., Lee W.C.: Single-machine scheduling with deteriorating jobs and setup times to minimize the maximum tardiness. Comput. Oper. Res. 38, 1760–1765 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cheng T.C.E., Hsu C.J., Yang D.L.: Unrelated parallel-machine scheduling with deteriorating maintenance activities. Comput. Ind. Eng. 60, 602–605 (2011)

    Article  Google Scholar 

  9. Cheng T.C.E., Lee W.C., Wu C.C.: Single-machine scheduling with deteriorating jobs and past-sequence-dependent setup times. Appl. Math. Model. 35, 1861–1867 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  10. Cheng T.C.E., Yang S.J., Yang D.L.: Common due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity. Int. J. Prod. Econ. 135, 154–161 (2012)

    Article  Google Scholar 

  11. Discenzo, F.M., Rusnak, D., Hanson, L., Chung, D., Zevchek, J.: Next generation pump systems enable new opportunities for asset management and economic optimization. In: Proceedings of the 19th International Pump Users Symposium (Houston) (2002)

  12. Gawiejnowicz S.: Time-Dependent Scheduling. Springer, Berlin (2008)

    MATH  Google Scholar 

  13. Gupta J.N.D., Gupta S.K.: Single facility scheduling with nonlinear processing times. Comput. Ind. Eng. 14(4), 387–393 (1988)

    Article  Google Scholar 

  14. Huang X., Wang M.Z.: Parallel identical machines scheduling with deteriorating jobs and total absolute differences penalties. Appl. Math. Model. 35, 1349–1353 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. 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 

  16. Lai, P.J., Wu, C.C., Lee, W.C.: Single-machine scheduling with logarithm deterioration. Optim. Lett. doi:10.1007/s11590-011-0362-7 (2011)

  17. Lee, W.C.: Single-machine scheduling with past-sequence-dependent setup times and general effects of deterioration and learning. Optim. Lett. doi:10.1007/s11590-012-0481-9 (2012)

  18. Lee W.C., Lai P.J., Wu C.C.: Some single-machine and flowshop scheduling problems with a non-linear deterioration function. Comput. Math. Appl. 62, 2487–2496 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  19. Lee W.C., Lin J.B., Shiau Y.R.: Deteriorating job scheduling to minimize the number of late jobs with setup times. Comput. Ind. Eng. 61, 782–787 (2011)

    Article  Google Scholar 

  20. Lee W.C., Lu Z.S.: Group scheduling with deteriorating jobs to minimize the total weighted number of late jobs. Appl. Math. Comput. 218, 8750–8757 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  21. Li S.S., Ng C.T., Yuan J.J.: Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine. Int. J. Prod. Econ. 131, 747–751 (2011)

    Article  Google Scholar 

  22. Miao C.X., Zhang Y.Z., Cao Z.G.: Bounded parallel-batch scheduling on single and multi machines for deteriorating jobs. Inform. Process. Lett. 111, 798–803 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  23. Ng C.T., Wang J.B., Cheng T.C.E., Lam S.S.: Flowshop scheduling of deteriorating jobs on dominating machines. Comput. Ind. Eng. 61, 647–654 (2011)

    Article  Google Scholar 

  24. Pinedo M.: Scheduling: Theory, Algorithms, and Systems. Prentice-Hall, Upper Saddle River (2008)

    Google Scholar 

  25. Rudek A., Rudek R.: A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models. Comput. Math. Appl. 62, 1870–1878 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  26. Wang, L.Y., Huang, X., Ji, P., Feng, E.M.: Unrelated parallel-machine scheduling with deteriorating maintenance activities to minimize the total completion time. Optim. Lett. doi:10.1007/s11590-012-0472-x (2012)

  27. Wang, J.B., Ji, P., Cheng, T.C.E., Wang, D.: Minimizing makespan in a two-machine flow shop with effects of deterioration and learning. Optim. Lett. doi:10.1007/s11590-011-0334-y (2011)

  28. Wang J.B., Sun L.H., Sun L.Y.: Single-machine total completion time scheduling with a time-dependent deterioration. Appl. Math. Model. 35, 1506–1511 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  29. Wang J.B., Wang C.: Single-machine due-window assignment problem with learning effect and deteriorating jobs. Appl. Math. Model. 35, 4017–4022 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  30. Wang J.B., Wang M.Z.: Single-machine scheduling with nonlinear deterioration. Optim. Lett. 6, 87–98 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  31. Wang J.B., Wei C.M.: Parallel machine scheduling with a deteriorating maintenance activity and total absolute differences penalties. Appl. Math. Comput. 217, 8093–8099 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  32. Welte, T.M., Vatn, J., Heggest, J.: Markov state model for optimization of maintenance and renewal of hydro power components. In: International Conference on Probabilistic Methods Applied to Power Systems, pp. 1–7 (2006)

  33. Yang D.L., Cheng T.C.E., Yang S.J., Hsu C.J.: Unrelated parallel-machine scheduling with aging effects and multi-maintenance activities. Comput. Oper. Res. 39, 1458–1464 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  34. Yang S.H., Wang J.B.: Minimizing total weighted completion time in a two-machine flow shop scheduling under simple linear deterioration. Appl. Math. Comput. 217, 4819–4826 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  35. Zhao C.L., Hsu C.J., Yang D.L.: Considerations of single-machine scheduling with deteriorating jobs. Appl. Math. Model. 35(10), 5134–5142 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  36. Zhao C.L., Tang H.Y.: A note to due-window assignment and single machine scheduling with deteriorating jobs and a rate-modifying activity. Comput. Oper. Res. 39, 1300–1303 (2012)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Wen-Chiung Lee.

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Cheng, T.C.E., Tseng, SC., Lai, PJ. et al. Single-machine scheduling with accelerating deterioration effects. Optim Lett 8, 543–554 (2014). https://doi.org/10.1007/s11590-012-0539-8

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