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Mathematical Problems in Engineering
Volume 2013, Article ID 972358, 9 pages
http://dx.doi.org/10.1155/2013/972358
Research Article

Scheduling with Learning Effects and/or Time-Dependent Processing Times to Minimize the Weighted Number of Tardy Jobs on a Single Machine

Operations Management Area, DeGroote School of Business, McMaster University, Hamilton, ON, Canada L8S 4L8

Received 2 August 2013; Revised 23 October 2013; Accepted 23 October 2013

Academic Editor: Chin-Chia Wu

Copyright © 2013 Jianbo Qian and George Steiner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. P. Wright, “Factors affecting the cost of airplanes,” Journal of Aeronautical Sciences, vol. 3, pp. 122–128, 1936. View at Publisher · View at Google Scholar
  2. G. K. Webb, “Integrated circuit (IC) pricing,” Journal of High Technology Management Research, vol. 5, no. 2, pp. 247–260, 1994. View at Publisher · View at Google Scholar · View at Scopus
  3. C. Sáenz-Royo and V. Salas-Fumás, “Learning to learn and productivity growth: evidence from a new car-assembly plant,” Omega, vol. 41, no. 2, pp. 336–344, 2013. View at Publisher · View at Google Scholar
  4. S. Gawiejnowicz, “A note on scheduling on a single processor with speed dependent on a number of executed jobs,” Information Processing Letters, vol. 57, no. 6, pp. 297–300, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Biskup, “Single-machine scheduling with learning considerations,” European Journal of Operational Research, vol. 115, no. 1, pp. 173–178, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. V. S. Gordon, C. N. Potts, V. A. Strusevich, and J. D. Whitehead, “Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation,” Journal of Scheduling, vol. 11, no. 5, pp. 357–370, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. Mosheiov, “Parallel machine scheduling with a learning effect,” Journal of the Operational Research Society, vol. 52, no. 10, pp. 1165–1169, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. G. Mosheiov and J. B. Sidney, “Note on scheduling with general learning curves to minimize the number of tardy jobs,” Journal of the Operational Research Society, vol. 56, no. 1, pp. 110–112, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. D. Okołowski and S. Gawiejnowicz, “Exact and heuristic algorithms for parallel-machine scheduling with de Jong's learning effect,” Computers and Industrial Engineering, vol. 59, no. 2, pp. 272–279, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Biskup, “A state-of-the-art review on scheduling with learning effects,” European Journal of Operational Research, vol. 188, no. 2, pp. 315–329, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Janiak and R. Rudek, “Scheduling problems with position dependent job processing times,” in Scheduling in Computer and Manufacturing Systems, A. Janiak, Ed., pp. 26–38, Wydawnictwa Komunikacji i Łączności, Wroclaw, Poland, 2006. View at Google Scholar
  12. A. Janiak, T. Krysiak, and R. Trela, “Scheduling problems with learning and ageing effects: a survey,” Decision Making in Manufacturing and Services, vol. 5, no. 1-2, pp. 19–36, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K. Rustogi and V. A. Strusevich, “Simple matching vs linear assignment in scheduling models with positional effects: a critical review,” European Journal of Operational Research, vol. 222, no. 3, pp. 393–407, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. K. Gupta, A. S. Kunnathur, and K. Dandapani, “Optimal repayment policies for multiple loans,” Omega, vol. 15, no. 4, pp. 323–330, 1987. View at Publisher · View at Google Scholar · View at Scopus
  15. N. P. Rachaniotis and C. P. Pappis, “Scheduling fire-fighting tasks using the concept of ‘deteriorating jobs’,” Canadian Journal of Forest Research, vol. 36, no. 3, pp. 652–658, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. A. S. Kunnathur and S. K. Gupta, “Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem,” European Journal of Operational Research, vol. 47, no. 1, pp. 56–64, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. G. Mosheiov, “-shaped policies to schedule deteriorating jobs,” Journal of the Operational Research Society, vol. 47, no. 9, pp. 1184–1191, 1996. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Browne and U. Yechiali, “Scheduling deteriorating jobs on a single processor,” Operations Research, vol. 38, no. 3, pp. 495–498, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. G. Mosheiov, “V-shaped policies for scheduling deteriorating jobs,” Operations Research, vol. 39, no. 6, pp. 979–991, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. T. C. E. Cheng, Q. Ding, and B. M. T. Lin, “A concise survey of scheduling with time-dependent processing times,” European Journal of Operational Research, vol. 152, no. 1, pp. 1–13, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. Gawiejnowicz, Time-Dependent Scheduling, Springer, Berlin, Germany, 2008. View at MathSciNet
  22. W. C. Lee, “A note on deteriorating jobs and learning in single-machine scheduling problems,” International Journal of Business and Economics, vol. 3, no. 1, pp. 83–89, 2004. View at Google Scholar
  23. J.-B. Wang, “A note on scheduling problems with learning effect and deteriorating jobs,” International Journal of Systems Science, vol. 37, no. 12, pp. 827–833, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J.-B. Wang, “Single-machine scheduling problems with the effects of learning and deterioration,” Omega, vol. 35, no. 4, pp. 397–402, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. X. Wang and T. C. E. Cheng, “Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan,” European Journal of Operational Research, vol. 178, no. 1, pp. 57–70, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. L. Y. Wang, J. B. Wang, W. J. Guo, X. Huang, and E. M. Feng, “Two single-machine scheduling problems with the effects of deterioration and learning,” International Journal of Advanced Manufacturing Technology, vol. 46, no. 5–8, pp. 715–720, 2007. View at Publisher · View at Google Scholar
  27. J.-B. Wang and T. C. E. Cheng, “Scheduling problems with the effects of deterioration and learning,” Asia-Pacific Journal of Operational Research, vol. 24, no. 2, pp. 245–261, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. C. Koulamas, S. Gupta, and G. J. Kyparisis, “A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times,” European Journal of Operational Research, vol. 205, no. 2, pp. 479–482, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  29. Y. Leyvand, D. Shabtay, and G. Steiner, “A unified approach for scheduling with convex resource consumption functions using positional penalties,” European Journal of Operational Research, vol. 206, no. 2, pp. 301–312, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. J. Qian and G. Steiner, “Fast algorithms for scheduling with learning effects and time-dependent processing times on a single machine,” European Journal of Operational Research, vol. 225, no. 3, pp. 547–551, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  31. R. L. Graham, E. L. Lawler, J. K. Lenstra, and A. H. G. R. Kan, “Optimization and approximation in deterministic sequencing and scheduling: a survey,” Annals of Discrete Mathematics, vol. 5, pp. 287–326, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  32. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, NJ, USA, 1982. View at MathSciNet
  33. D. Shabtay and G. Steiner, “Two due date assignment problems in scheduling a single machine,” Operations Research Letters, vol. 34, no. 6, pp. 683–691, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. D. Shabtay and G. Steiner, “Optimal due date assignment and resource allocation to minimize the weighted number of tardy jobs on a single machine,” Manufacturing and Service Operations Management, vol. 9, no. 3, pp. 332–350, 2007. View at Publisher · View at Google Scholar · View at Scopus