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A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times

Author

Listed:
  • Hiroshi Kise

    (Kyoto Institute of Technology, Kyoto, Japan)

  • Toshihide Ibaraki

    (Kyoto University, Kyoto, Japan)

  • Hisashi Mine

    (Kyoto University, Kyoto, Japan)

Abstract

We consider a class of n -job one-machine scheduling problems with ready time r ( i ), processing time p ( i ), and due time d ( i ) for each job i . Preemption is not allowed, and precedence constraints among jobs are not assumed. For this problem we show that there is a 0( n 2 )-time algorithm to find a schedule that minimizes the number of tardy jobs, under the assumption that r ( i ) r ( j ) implies d ( i ) ≤ d ( j ).

Suggested Citation

  • Hiroshi Kise & Toshihide Ibaraki & Hisashi Mine, 1978. "A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times," Operations Research, INFORMS, vol. 26(1), pages 121-126, February.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:1:p:121-126
    DOI: 10.1287/opre.26.1.121
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    Cited by:

    1. Peridy, Laurent & Pinson, Eric & Rivreau, David, 2003. "Using short-term memory to minimize the weighted number of late jobs on a single machine," European Journal of Operational Research, Elsevier, vol. 148(3), pages 591-603, August.
    2. Federico Malucelli & Sara Nicoloso, 2007. "Shiftable intervals," Annals of Operations Research, Springer, vol. 150(1), pages 137-157, March.
    3. Mosheiov, Gur & Sarig, Assaf, 2010. "Minimum weighted number of tardy jobs on an m-machine flow-shop with a critical machine," European Journal of Operational Research, Elsevier, vol. 201(2), pages 404-408, March.
    4. Gupta, Jatinder N. D. & Ho, Johnny C., 1996. "Scheduling with two job classes and setup times to minimize the number of tardy jobs," International Journal of Production Economics, Elsevier, vol. 42(3), pages 205-216, April.
    5. Gio Kao & Edward Sewell & Sheldon Jacobson & Shane Hall, 2012. "New dominance rules and exploration strategies for the 1|r i |∑U i scheduling problem," Computational Optimization and Applications, Springer, vol. 51(3), pages 1253-1274, April.
    6. Sevaux, Marc & Dauzere-Peres, Stephane, 2003. "Genetic algorithms to minimize the weighted number of late jobs on a single machine," European Journal of Operational Research, Elsevier, vol. 151(2), pages 296-306, December.
    7. François Clautiaux & Boris Detienne & Henri Lefebvre, 2023. "A two-stage robust approach for minimizing the weighted number of tardy jobs with objective uncertainty," Journal of Scheduling, Springer, vol. 26(2), pages 169-191, April.
    8. Xiaoqiang Cai & Sean Zhou, 1999. "Stochastic Scheduling on Parallel Machines Subject to Random Breakdowns to Minimize Expected Costs for Earliness and Tardy Jobs," Operations Research, INFORMS, vol. 47(3), pages 422-437, June.
    9. Asano, Makoto & Ohta, Hiroshi, 1996. "Single machine scheduling using dominance relation to minimize earliness subject to ready and due times," International Journal of Production Economics, Elsevier, vol. 44(1-2), pages 35-43, June.
    10. Leung, Joseph Y.-T. & Li, Haibing & Pinedo, Michael, 2006. "Scheduling orders for multiple product types with due date related objectives," European Journal of Operational Research, Elsevier, vol. 168(2), pages 370-389, January.
    11. Dauzere-Peres, Stephane, 1995. "Minimizing late jobs in the general one machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 81(1), pages 134-142, February.
    12. M'Hallah, Rym & Bulfin, R.L., 2007. "Minimizing the weighted number of tardy jobs on a single machine with release dates," European Journal of Operational Research, Elsevier, vol. 176(2), pages 727-744, January.
    13. Baptiste, Philippe & Peridy, Laurent & Pinson, Eric, 2003. "A branch and bound to minimize the number of late jobs on a single machine with release time constraints," European Journal of Operational Research, Elsevier, vol. 144(1), pages 1-11, January.
    14. Stéphane Dauzère‐Pérès & Marc Sevaux, 2003. "Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(3), pages 273-288, April.
    15. Detienne, Boris, 2014. "A mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints," European Journal of Operational Research, Elsevier, vol. 235(3), pages 540-552.
    16. Koulamas, Christos & Kyparisis, George J., 2001. "Single machine scheduling with release times, deadlines and tardiness objectives," European Journal of Operational Research, Elsevier, vol. 133(2), pages 447-453, January.
    17. Cai, X. & Lum, V. Y. S. & Chan, J. M. T., 1997. "Scheduling about a common due date with kob-dependent asymmetric earliness and tardiness penalties," European Journal of Operational Research, Elsevier, vol. 98(1), pages 154-168, April.
    18. Zhenming Chen & Vikas Singh & Jinhui Xu, 2005. "Efficient Job Scheduling Algorithms with Multi-Type Contentions," Journal of Combinatorial Optimization, Springer, vol. 10(2), pages 179-197, September.
    19. Sadykov, Ruslan, 2008. "A branch-and-check algorithm for minimizing the weighted number of late jobs on a single machine with release dates," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1284-1304, September.
    20. I. Adiri & E. Frostig & A. H. G. Rinnooy Kan, 1991. "Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 261-271, April.

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