Journal of Global Optimization

, Volume 54, Issue 2, pp 389–404 | Cite as

Scheduling linear deteriorating jobs to minimize the number of tardy jobs

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Abstract

In this paper a problem of scheduling a single machine under linear deterioration which aims at minimizing the number of tardy jobs is considered. According to our assumption, processing time of each job is dependent on its starting time based on a linear function where all the jobs have the same deterioration rate. It is proved that the problem is NP-hard; hence a branch and bound procedure and a heuristic algorithm with O(n 2) is proposed where the heuristic one is utilized for obtaining the upper bound of the B&B procedure. Computational results for 1,800 sample problems demonstrate that the B&B method can solve problems with 28 jobs quickly and in some other groups larger problems are also solved. Generally, B&B method can optimally solve 85% of the samples which shows high performance of the proposed method. Also it is shown that the average value of the ratio of optimal solution to the heuristic algorithm result with the objective ∑(1 − Ui) is at most 1.11 which is more efficient in comparison to other proposed algorithms in related studies in the literature.

Keywords

Scheduling Linear deteriorating jobs Branch and bound Number of tardy jobs 
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References

  1. 1.
    Bachman A., Janiak A.: Minimizing maximum lateness under linear deterioration theory and methodology. Eur. J. Oper. Res. 126, 557–566 (2000)CrossRefGoogle Scholar
  2. 2.
    Wang J.B., Wang L.Y., Wang D., Gao W.J.: Single-machine group scheduling with general linear deterioration to minimize the makespan. Int. J. Adv. Manuf. Technol. 43, 146–150 (2009)CrossRefGoogle Scholar
  3. 3.
    Cheng T.C.E., Ding Q.: The complexity of scheduling starting time dependent tasks with release times. Inf. Proces. Lett. 65, 75–79 (1998)CrossRefGoogle Scholar
  4. 4.
    Mosheiov G.: Scheduling jobs under simple linear deterioration. Comput. Oper. Res. 21, 653–659 (1994)CrossRefGoogle Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Gupta J.N.D., Gupta S.K.: Single facility scheduling with nonlinear processing times. Comput. Ind. Eng. 14, 387–393 (1988)CrossRefGoogle Scholar
  7. 7.
    Lee W.C., Wu C.C., Chung Y.H.: Scheduling deteriorating jobs on a single machine with release times. Comput. Ind. Eng. 54, 441–452 (2008)CrossRefGoogle Scholar
  8. 8.
    Wu C.C., Lee W.C.: Scheduling linear deteriorating jobs to minimize makespan with an availability constraint on a single machine. Inf. Proces. Lett. 87, 89–93 (2003)CrossRefGoogle Scholar
  9. 9.
    Ji M., He Y., Cheng T.C.E.: Scheduling linear deteriorating jobs with an availability constraint on a single machine. Theor. Comput. Sci. 362, 115–126 (2006)CrossRefGoogle Scholar
  10. 10.
    Browne S., Yechiali U.: Scheduling deteriorating jobs on a single processor. Comput. Oper. Res. 38, 495–498 (1990)Google Scholar
  11. 11.
    Bachman A., Janiak A.: Scheduling Jobs with Special Type of Start Time Dependent Processing Times. Institute of Engineering Cybernetics. Wroclaw University of Technology, Wroclaw (1997)Google Scholar
  12. 12.
    Hsu Y.S., Lin B.M.T.: Minimization of maximum lateness under linear deterioration. Omega 31, 459–469 (2003)CrossRefGoogle Scholar
  13. 13.
    Bachman A., Janiak A., Kovalyov M.Y.: Minimizing the total weighted completion time of deteriorating jobs. Inf. Proces. Lett. 81, 81–84 (2002)CrossRefGoogle Scholar
  14. 14.
    Moslehi G., Jafari A.: Minimizing the number of tardy jobs under piecewise-linear deterioration. Comput. Ind. Eng. 59, 573–584 (2010)CrossRefGoogle Scholar
  15. 15.
    Lai, P., Wu, C., Lee, W.: Single machine scheduling with logarithm deterioration. Optim. Lett. (2011). doi: 10.1007/s11590-011-0362-7
  16. 16.
    Lee C., Yu G.: Parallel machine scheduling under potential disruption. Optim. Lett. 2, 27–37 (2008)CrossRefGoogle Scholar
  17. 17.
    M’Hallah R., Bulfin R.L.: Minimizing the weighted number of tardy jobs on a single machine with release dates. Eur. J. Oper. Res. 176, 727–744 (2007)CrossRefGoogle Scholar
  18. 18.
    Peres S.D., Sevaux M.: An exact method to minimize the number of tardy jobs in single machine scheduling. J. Sched. 7, 405–420 (2004)CrossRefGoogle Scholar
  19. 19.
    Bulfin R.L., M’Hallah R.: Minimizing the weighted number of tardy jobs on a two-machine flowshop. Comput. Oper. Res. 30, 1887–1900 (2003)CrossRefGoogle Scholar
  20. 20.
    M’Hallah R., Bulfin R.L.: Minimizing the weighted number of tardy jobs on a single machine. Eur. J. Oper. Res. 145, 45–56 (2003)CrossRefGoogle Scholar
  21. 21.
    Chen W.J.: Minimizing number of tardy jobs on a single machine subject to periodic maintenance. Omega 37, 591–599 (2009)CrossRefGoogle Scholar
  22. 22.
    Brucker P.: Scheduling Algorithm, 5th edn. Springer Publishing Company, New York (2006)Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringIsfahan University of TechnologyIsfahanIran

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