Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 547573, 8 pages
http://dx.doi.org/10.1155/2014/547573
Research Article

Best Possible Approximation Algorithms for Single Machine Scheduling with Increasing Linear Maintenance Durations

School of Science, East China Institute of Technology, Nanchang, Jiangxi 330013, China

Received 6 November 2013; Accepted 19 December 2013; Published 13 February 2014

Academic Editors: J. G. Barbosa and D. Oron

Copyright © 2014 Xuefei Shi and Dehua Xu. 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. G. Schmidt, “Scheduling with limited machine availability,” European Journal of Operational Research, vol. 121, no. 1, pp. 1–15, 2000. View at Publisher · View at Google Scholar · View at Scopus
  2. C.-Y. Lee, “Machine scheduling with availability constraints,” in Handbook of Scheduling: Algorithms, Models and Performance Analysis, J. Y.-T. Leung, Ed., pp. 22.1–22.13, CRC Press, Boca Raton, Fla, USA, 2004. View at Google Scholar
  3. M. Ji, Y. He, and T. C. E. Cheng, “Single-machine scheduling with periodic maintenance to minimize makespan,” Computers & Operations Research, vol. 34, no. 6, pp. 1764–1770, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. Ma, C. Chu, and C. Zuo, “A survey of scheduling with deterministic machine availability constraints,” Computers & Industrial Engineering, vol. 58, no. 2, pp. 199–211, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. K. Sun and H. Li, “Scheduling problems with multiple maintenance activities and non-preemptive jobs on two identical parallel machines,” International Journal of Production Economics, vol. 124, no. 1, pp. 151–158, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. C.-J. Hsu, T. C. E. Cheng, and D.-L. Yang, “Unrelated parallel-machine scheduling with rate-modifying activities to minimize the total completion time,” Information Sciences, vol. 181, no. 20, pp. 4799–4803, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Bock, D. Briskorn, and A. Horbach, “Scheduling flexible maintenance activities subject to job-dependent machine deterioration,” Journal of Scheduling, vol. 15, pp. 565–578, 2012. View at Publisher · View at Google Scholar · View at Scopus
  8. V. Gordon, V. Strusevich, and A. Dolgui, “Scheduling with due date assignment under special conditions on job processing,” Journal of Scheduling, vol. 15, pp. 447–456, 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. B. Mor and G. Mosheiov, “Scheduling a maintenance activity and due-window assignment based on common flow allowance,” International Journal of Production Economics, vol. 135, no. 1, pp. 222–230, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Xu, M. Liu, Y. Yin, and J. Hao, “Scheduling tool changes and special jobs on a single machine to minimize makespan,” Omega, vol. 41, pp. 299–304, 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Xu and D.-L. Yang, “Makespan minimization for two parallel machines scheduling with a periodic availability constraint: mathematical programming model, average-case analysis, and anomalies,” Applied Mathematical Modelling, vol. 37, pp. 7561–7567, 2013. View at Publisher · View at Google Scholar
  12. D.-L. Yang and S.-J. Yang, “Unrelated parallel-machine scheduling with multiple rate-modifying activities,” Information Sciences, vol. 235, pp. 280–286, 2013. View at Publisher · View at Google Scholar
  13. S.-J. Yang, “Unrelated parallel-machine scheduling with deterioration effects and deteriorating multimaintenance activities for minimizing the total completion time,” Applied Mathematical Modelling, vol. 37, pp. 2995–3005, 2013. View at Publisher · View at Google Scholar
  14. D. Xu, Y. Yin, and H. Li, “Scheduling jobs under increasing linear machine maintenance time,” Journal of Scheduling, vol. 13, no. 4, pp. 443–449, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. 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 Scopus
  16. E. G. Coffman Jr., M. R. Garey, and D. S. Johnson, “Approximation algorithms for bin packing: a survey,” in Approximation Algorithms for NP-Hard Problems, D. S. Hochbaum, Ed., pp. 46–93, PWS, Boston, Mass, USA, 1997. View at Google Scholar
  17. M. Pinedo, Scheduling: Theory, Algorithms, and Systems, Springer, New York, NY, USA, 4th edition, 2012.
  18. D. Simchi-Levi, “New worst-case results for the bin-packing problem,” Naval Research Logistics, vol. 41, no. 4, pp. 579–585, 1994. View at Google Scholar · View at Scopus
  19. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, New York, NY, USA, 1979.