Journal of Scheduling

, Volume 12, Issue 5, pp 543–553 | Cite as

Conjugate problems in time-dependent scheduling

  • Stanisław Gawiejnowicz
  • Wiesław Kurc
  • Lidia Pankowska
Article

Abstract

In the paper, we consider conjugate problems which constitute a new class of mutually related time-dependent scheduling problems. Any element from this class is a composite problem, being a pair of two time-dependent scheduling problems connected by a conjugacy formula. We prove basic properties of conjugate problems and show the relations that hold between such problems. We also propose an approach to the construction of greedy heuristics for the conjugate problems. We illustrate applications of the results by examples.

Keywords

Time-dependent scheduling Conjugate problems Heuristic algorithms 

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References

  1. Alidaee, B., & Womer, N. K. (1999). Scheduling with time dependent processing times: Review and extensions. Journal of the Operational Research Society, 50, 711–720. CrossRefGoogle Scholar
  2. Bachman, A., & Janiak, A. (2004). Scheduling jobs with position-dependent processing times. Journal of the Operational Research Society, 55, 257–264. CrossRefGoogle Scholar
  3. Bachman, A., Janiak, A., & Kovalyov, M. Y. (2002a). Minimizing the total weighted completion time of deteriorating jobs. Information Processing Letters, 81, 81–84. CrossRefGoogle Scholar
  4. Bachman, A., Cheng, T.-C. E., Janiak, A., & Ng, C.-T. (2002b). Scheduling start time dependent jobs to minimize the total weighted completion time. Journal of the Operational Research Society, 53, 688–693. CrossRefGoogle Scholar
  5. Biskup, D. (2008). A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research, 188, 315–329. CrossRefGoogle Scholar
  6. Błażewicz, J., & Gawiejnowicz, S. (1999). Scheduling tasks and vehicles in a flexible manufacturing system subject to mean flow time minimization. Foundations of Computing and Decision Sciences, 24, 1–12. Google Scholar
  7. Brucker, P. (2007). Scheduling algorithms (5th ed.). Berlin: Springer. Google Scholar
  8. Cheng, T.-C. E., & Ding, Q. (1998). The complexity of scheduling starting time dependent tasks with release times. Information Processing Letters, 65, 75–79. CrossRefGoogle Scholar
  9. Cheng, T.-C. E., Ding, Q., & Lin, B. M.-T. (2004). A concise survey of scheduling with time-dependent scheduling times. European Journal of Operational Research, 152, 1–13. CrossRefGoogle Scholar
  10. Conway, R. W., Maxwell, W. L., & Miller, L. W. (1967). Theory of scheduling. Reading: Addison-Wesley. Google Scholar
  11. Gawiejnowicz, S. (1996a). A note on scheduling on a single processor with speed dependent on a number of executed jobs. Information Processing Letters, 57, 297–300. CrossRefGoogle Scholar
  12. Gawiejnowicz, S. (1996b). Brief survey of continuous models of scheduling. Foundations of Computing and Decision Sciences, 21, 81–100. Google Scholar
  13. Gawiejnowicz, S. (2008). Time-dependent scheduling. Monographs in theoretical computer science. An EATCS Series. Springer, Berlin. Google Scholar
  14. Gawiejnowicz, S., Kurc, W., & Pankowska, L. (2002). A greedy approach for a time-dependent scheduling problem. In Lecture notes in computer science (Vol. 2328, pp. 79–86). Google Scholar
  15. Gawiejnowicz, S., Kurc, W., & Pankowska, L. (2006). Analysis of a time-dependent scheduling problem by signatures of deterioration rate sequences. Discrete Applied Mathematics, 154, 2150–2166. CrossRefGoogle Scholar
  16. Gawiejnowicz, S., Kurc, W., & Pankowska, L. (2008). Equivalent time-dependent scheduling problems. European Journal of Operational Research, 196, 919–929. CrossRefGoogle Scholar
  17. Gupta, S. K., Kunnathur, A. S., & Dandapani, K. (1987). Optimal repayment policies for multiple loans. Omega, 15, 323–330. CrossRefGoogle Scholar
  18. Ho, K. I.-J., Leung, J. Y.-T., & Wei, W.-D. (1993). Complexity of scheduling tasks with time-dependent execution times. Information Processing Letters, 48, 315–320. CrossRefGoogle Scholar
  19. Janiak, A. (1988). General flow-shop scheduling with resource constraints. International Journal of Production Research, 26, 1089–1103. CrossRefGoogle Scholar
  20. Mosheiov, G. (1995). Scheduling jobs with step-deterioration; Minimizing makespan on a single- and multi-machine. Computers and Industrial Engineering, 28, 869–879. CrossRefGoogle Scholar
  21. Sriskandarajah, C., & Goyal, S. K. (1989). Scheduling of a two-machine flowshop with processing time linearly dependent on job waiting-time. Journal of the Operational Research Society, 40, 907–921. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Stanisław Gawiejnowicz
    • 1
  • Wiesław Kurc
    • 1
  • Lidia Pankowska
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland

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