Advertisement

Single-Machine Scheduling Problems Simultaneous with Deteriorating and Learning Effects Under a Deteriorating Maintenance Consideration

  • Suh-Jenq YangEmail author
  • Dar-Li Yang
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 60)

Abstract

Machine scheduling problems in just-in-time production environments are important issues in modern operations management to satisfy customer demand for superior service. In this paper, we investigate single-machine scheduling problems with simultaneous considerations of the effects of deterioration and learning. Due to the deteriorating effect, maintenance may be performed on the machine to improve its production efficiency. We assume that at most one maintenance is allowed throughout the scheduling horizon. We further assume that the maintenance duration depends on its starting time. Our goal is to find jointly the optimal time to perform the maintenance, the optimal location of the due-window, and the optimal job sequence such that the total cost that includes earliness, tardiness, and due-window size and location penalties is minimized. We also aim to investigate the makespan, the total completion time, and the total absolute deviation of completion times minimization problems. We propose polynomial time algorithms for all the studied problems.

Keywords

Schedule Problem Completion Time Polynomial Time Algorithm Total Completion Time Short Processing Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We thank the editors and the anonymous reviewers for their helpful comments and suggestions on an earlier version of the paper. This research was supported by the National Science Council of Taiwan, Republic of China, under grant number NSC 100-2221-E-252-002-MY2.

References

  1. 1.
    Alidaee, B., Womer, N.: Scheduling with time dependent processing times: Review and extensions. Journal of the Operational Research Society 50, 711–729 (1999)zbMATHGoogle Scholar
  2. 2.
    Bachman, A., Janiak, A.: Scheduling jobs with position-dependent processing times. Journal of the Operational Research Society 55, 257–264 (2004)zbMATHCrossRefGoogle Scholar
  3. 3.
    Biskup, D.: Single-machine scheduling with learning considerations. European Journal of Operational Research 115, 173–178 (1999)zbMATHCrossRefGoogle Scholar
  4. 4.
    Biskup, D.: A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research 188, 315–329 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Browne, S., Yechiali, U.: Scheduling deteriorating jobs on a single processor. Operations Research 38, 495–498 (1990)zbMATHCrossRefGoogle Scholar
  6. 6.
    Cheng, T.C.E.: Optimal common due-date with limited completion time deviation. Computers & Operations Research 15, 91–96 (1988)zbMATHCrossRefGoogle Scholar
  7. 7.
    Cheng, T.C.E., Ding, Q., Lin, B.: A concise survey of scheduling with time-dependent processing times. European Journal of Operational Research 152, 1–13 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Cheng, T.C.E., Kang, L., Ng, C.: Due-date assignment and single machine scheduling with deteriorating jobs. Journal of the Operational Research Society 55, 198–203 (2004)zbMATHCrossRefGoogle Scholar
  9. 9.
    Cheng, T.C.E., Kovalyov, M.: Scheduling with learning effects on job processing times. Working Paper 06/94, Faculty of Business and Information Systems, The Hong Kong Polytechnic University (1994)Google Scholar
  10. 10.
    Cheng, T.C.E., Wang, G.: Single machine scheduling with learning effect considerations. Annals of Operations Research 98, 273–290 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    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. International Journal of Production Economics doi:10.1016/j.ijpe.2010.10.005Google Scholar
  12. 12.
    Gawiejnowicz, S.: A note on scheduling on a single processor with speed dependent on a number of executed jobs. Information Processing Letters 56, 297–300 (1996)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Gawiejnowicz, S.: Scheduling deteriorating jobs subject to job or machine availability constraints. European Journal of Operational Research 180, 472–478 (2007)zbMATHCrossRefGoogle Scholar
  14. 14.
    Gawiejnowicz, S.: Time-dependent Scheduling. Springer-Verlag, New York (2008)zbMATHGoogle Scholar
  15. 15.
    Gawiejnowicz, S., Kononov, A.: Complexity and approximability of scheduling resumable proportionally deteriorating jobs. European Journal of Operational Research 200, 305–308 (2010)zbMATHCrossRefGoogle Scholar
  16. 16.
    Graham, R., Lawler, E., J.K., L., Rinnooy Kan, A.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics 5, 287–326 (1979)Google Scholar
  17. 17.
    Gupta, J., Gupta, S.: Single facility scheduling with nonlinear processing times. Computers and Industrial Engineering 14, 387–393 (1988)CrossRefGoogle Scholar
  18. 18.
    Hardy, G., Littlewood, J., Polya, G.: Inequalities. Cambridge University Press, London (1967)Google Scholar
  19. 19.
    Hsu, C.J., Low, C., Su, C.T.: Single-machine scheduling problem with an availability constraint under simple linear deterioration. Journal of the Chinese Institute of Industrial Engineers 27, 189–198 (2010)CrossRefGoogle Scholar
  20. 20.
    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. Computers and Industrial Engineering 58, 58–63 (2010)CrossRefGoogle Scholar
  21. 21.
    Janiak, A., Kovalyov, M.Y.: Scheduling deteriorating jobs. In: A. Janiak (ed.) Scheduling in Computer and Manufacturing Systems, pp. 12–25. WKL, Warszawa, Poland (2006)Google Scholar
  22. 22.
    Janiak, A., Rudek, R.: Scheduling problems with position dependent job processing times. In: A. Janiak (ed.) Scheduling in Computer and Manufacturing Systems, pp. 26–32. WKL, Warszawa, Poland (2006)Google Scholar
  23. 23.
    Janiak, A., Rudek, R.: Experience based approach to scheduling problems with the learning effect. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 39, 344–357 (2009)CrossRefGoogle Scholar
  24. 24.
    Ji, M., He, Y., Cheng, T.C.E.: Scheduling linear deteriorating jobs with an availability constraint on a single machine. Theoretical Computer Science 362, 115–126 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Kanet, J.: Minimizing variation of flow time in single machine systems. Management Science 27, 1453–1459 (1981)zbMATHCrossRefGoogle Scholar
  26. 26.
    Kubzin, M., Strusevich, V.: Two-machine flow shop no-wait scheduling with machine maintenance. 4OR: A Quarterly Journal of Operations Research 3, 303–313 (2005)Google Scholar
  27. 27.
    Kubzin, M., Strusevich, V.: Planning machine maintenance in two-machine shop scheduling. Operations Research 54, 789–800 (2006)zbMATHCrossRefGoogle Scholar
  28. 28.
    Kunnathur, A., Gupta, S.: Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem. European Journal of Operational Research 47, 56–64 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Kuo, W.H., Yang, D.L.: Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect. European Journal of Operational Research 174, 1184–1190 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Lee, I.S.: Single machine scheduling with controllable processing times: A parametric study. International Journal of Production Economics 22, 105–110 (1991)CrossRefGoogle Scholar
  31. 31.
    Lee, W.C.: A note on deteriorating jobs and learning in single-machine scheduling problems. International Journal of Business and Economics 3, 83–89 (2004)Google Scholar
  32. 32.
    Liman, S., Ramaswamy, S.: Earliness-tardiness scheduling problems with a common delivery window. Operations Research Letters 15, 195–203 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Liman, S., Panwalkar, S.S., Thongmee, S.: Determination of common due window location in a single machine scheduling problem. European Journal of Operational Research 93, 68–74 (1996)zbMATHCrossRefGoogle Scholar
  34. 34.
    Liman, S., Panwalkar, S.S., Thongmee, S.: Common due window size and location determination in a single machine scheduling problem. Journal of the Operational Research Society 49, 1007–1010 (1998)zbMATHGoogle Scholar
  35. 35.
    Lodree Jr., E., Geiger, C.: A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration. European Journal of Operational Research 201, 644–648 (2010)zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Low, C., Hsu, C.J., Su, C.T.: Minimizing the makespan with an availability constraint on a single machine under simple linear deterioration. Computers & Mathematics with Applications 56, 257–265 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Ma, Y., Chu, C., Zuo, C.: A survey of scheduling with deterministic machine availability constraints. Computers and Industrial Engineering 58, 199–211 (2010)CrossRefGoogle Scholar
  38. 38.
    Mosheiov, G.: Scheduling jobs with step-deterioration: Minimizing makespan on a single- and multi-machine. Computers and Industrial Engineering 28, 869–879 (1995)CrossRefGoogle Scholar
  39. 39.
    Mosheiov, G., Sarig, A.: A due-window assignment problem with position-dependent processing times. Journal of the Operational Research Society 59, 997–1003 (2008)zbMATHCrossRefGoogle Scholar
  40. 40.
    Mosheiov, G., Sarig, A.: Scheduling a maintenance activity and due-window assignment on a single machine. Computers & Operations Research 36, 2541–2545 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  41. 41.
    Mosheiov, G., Sidney, J.: Scheduling with general job-dependent learning curves. European Journal of Operational Research 147, 665–670 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  42. 42.
    Mosheiov, G., Sidney, J.: Scheduling a deteriorating maintenance activity on a single machine. Journal of the Operational Research Society 61, 882–887 (2010)zbMATHCrossRefGoogle Scholar
  43. 43.
    Panwalkar, S., Smith, M., Seidmann, A.: Common due date assignment to minimize total penalty for the one machine scheduling problem. Operations Research 30, 391–399 (1982)zbMATHCrossRefGoogle Scholar
  44. 44.
    Sanlaville, E., Schmidt, G.: Machine scheduling with availability constraints. Acta Informatica 9, 795–811 (1998)CrossRefMathSciNetGoogle Scholar
  45. 45.
    Schmidt, G.: Scheduling with limited machine availability. European Journal of Operational Research 121, 1–15 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  46. 46.
    Sun, L.: Single-machine scheduling problems with deteriorating jobs and learning effects. Computers and Industrial Engineering 57, 843–846 (2009)CrossRefGoogle Scholar
  47. 47.
    Toksar, M., Oron, D., Güner, E.: Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning. Computers & Mathematics with Applications 50, 401–406 (2009)Google Scholar
  48. 48.
    Wang, J.B.: A note on scheduling problems with learning effect and deteriorating jobs. International Journal of Systems Science 37, 827–833 (2006)zbMATHCrossRefGoogle Scholar
  49. 49.
    Wang, J.B.: Single-machine scheduling problems with the effects of learning and deterioration. Omega 35, 397–402 (2007)CrossRefGoogle Scholar
  50. 50.
    Wang, J.B.: Single machine scheduling with learning effect and deteriorating jobs. Computers and Industrial Engineering 57, 1452–1456 (2009)CrossRefGoogle Scholar
  51. 51.
    Wang, J.B.: Single machine scheduling with time-dependent learning effect and deteriorating jobs. Journal of the Operational Research Society 60, 583–586 (2009)CrossRefGoogle Scholar
  52. 52.
    Wang, J.B., Cheng, T.: Scheduling problems with the effects of deterioration and learning. Asia-pacific Journal of Operational Research 24, 245–261 (2007)CrossRefMathSciNetGoogle Scholar
  53. 53.
    Wang, J.B., Huang, X., Wang, X.Y., Yin, N., Wang, L.Y.: Learning effect and deteriorating jobs in the single machine scheduling problems. Applied Mathematical Modelling 33, 3848–3853 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  54. 54.
    Wang, X., Cheng, T.C.E.: Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan. European Journal of Operational Research 178, 57–70 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  55. 55.
    Wu, C.C., Lee, W.C.: Scheduling linear deteriorating jobs to minimize makespan with an availability constraint on a single machine. Information Processing Letters 87, 89–93 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  56. 56.
    Yang, D.L., Kuo, W.H.: Single-machine scheduling with both deterioration and learning effects. Annals of Operations Research 172, 315–327 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  57. 57.
    Yang, D.L., Kuo, W.H.: Some scheduling problems with deteriorating jobs and learning effects. Computers and Industrial Engineering 58, 25–28 (2010)CrossRefGoogle Scholar
  58. 58.
    Yang, S.J., Yang, D.L., Cheng, T.C.E.: Single-machine due-window assignment and scheduling with job-dependent aging effects and deteriorating maintenance. Computers & Operations Research 37, 1510–1514 (2010)zbMATHCrossRefMathSciNetGoogle Scholar
  59. 59.
    Yin, Y., Xu, D., Sun, K., Li, H.: Some scheduling problems with general position-dependent and time-dependent learning effects. Information Sciences 179, 2416–2425 (2009)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Industrial Engineering and ManagementNan Kai University of TechnologyNan-TouTaiwan
  2. 2.Department of Information ManagementNational Formosa UniversityYun-LinTaiwan

Personalised recommendations