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Scheduling with Deadlines and Loss Functions on k Parallel Machines

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  • James G. Root

    (The Ohio State University, Columbus)

Abstract

An optimal schedule is developed for H jobs on K identical machines in single stage production. The optimal schedule minimizes \sum b[max (0, A i - d i )] where A i is the actual completion time for job i and d i is the deadline for job i. A common deadline, t 0 , is assumed for all jobs, i.e., d i - t 0 , i - 1, ..., H.

Suggested Citation

  • James G. Root, 1965. "Scheduling with Deadlines and Loss Functions on k Parallel Machines," Management Science, INFORMS, vol. 11(3), pages 460-475, January.
    • Handle: RePEc:inm:ormnsc:v:11:y:1965:i:3:p:460-475
    DOI: 10.1287/mnsc.11.3.460
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    Citations

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    Cited by:

    1. Chen, Jeng-Fung & Wu, Tai-Hsi, 2006. "Total tardiness minimization on unrelated parallel machine scheduling with auxiliary equipment constraints," Omega, Elsevier, vol. 34(1), pages 81-89, January.
    2. Johnny C. Ho & Yih‐Long Chang, 1991. "Heuristics for minimizing mean tardiness for m parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 367-381, June.
    3. Christos Koulamas, 1997. "Decomposition and hybrid simulated annealing heuristics for the parallel‐machine total tardiness problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 109-125, February.
    4. Tanaka, Shunji & Araki, Mituhiko, 2008. "A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines," International Journal of Production Economics, Elsevier, vol. 113(1), pages 446-458, May.
    5. Shim, Sang-Oh & Kim, Yeong-Dae, 2007. "Scheduling on parallel identical machines to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 177(1), pages 135-146, February.
    6. Ronghua Meng & Yunqing Rao & Qiang Luo, 2020. "Modeling and solving for bi-objective cutting parallel machine scheduling problem," Annals of Operations Research, Springer, vol. 285(1), pages 223-245, February.
    7. Biskup, Dirk & Herrmann, Jan & Gupta, Jatinder N.D., 2008. "Scheduling identical parallel machines to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 115(1), pages 134-142, September.
    8. Azizoglu, Meral & Kirca, Omer, 1998. "Tardiness minimization on parallel machines," International Journal of Production Economics, Elsevier, vol. 55(2), pages 163-168, July.
    9. Yalaoui, Farouk & Chu, Chengbin, 2002. "Parallel machine scheduling to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 76(3), pages 265-279, April.
    10. Ho, Johnny C. & Chang, Yih-Long, 1995. "Minimizing the number of tardy jobs for m parallel machines," European Journal of Operational Research, Elsevier, vol. 84(2), pages 343-355, July.

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