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Note on Shim and Kim's lower bounds for scheduling on identical parallel machines to minimize total tardiness

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  • Schaller, Jeffrey

Abstract

This note introduces a new lower bound for the problem of scheduling on parallel identical machines to minimize total tardiness that is based on the concepts used in the two lower bounds developed by Shim and Kim [Shim, S.O., Kim, Y.D., 2007. Scheduling on parallel identical machines to minimize total tardiness. European Journal of Operational Research 177, 135-146]. The note shows that the new lower bound dominates the three lower bounds used in Shim and Kim's branch-and-bound algorithm and can be used in place of these lower bounds to lower the enumeration required.

Suggested Citation

  • Schaller, Jeffrey, 2009. "Note on Shim and Kim's lower bounds for scheduling on identical parallel machines to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 197(1), pages 422-426, August.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:1:p:422-426
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    References listed on IDEAS

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    1. Kim, Yeong-Dae, 1995. "Minimizing total tardiness in permutation flowshops," European Journal of Operational Research, Elsevier, vol. 85(3), pages 541-555, September.
    2. Azizoglu, Meral & Kirca, Omer, 1998. "Tardiness minimization on parallel machines," International Journal of Production Economics, Elsevier, vol. 55(2), pages 163-168, July.
    3. 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.
    4. 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.
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    Cited by:

    1. Herr, Oliver & Goel, Asvin, 2016. "Minimising total tardiness for a single machine scheduling problem with family setups and resource constraints," European Journal of Operational Research, Elsevier, vol. 248(1), pages 123-135.
    2. Asmaa Khoudi & Ali Berrichi, 2020. "Minimize total tardiness and machine unavailability on single machine scheduling problem: bi-objective branch and bound algorithm," Operational Research, Springer, vol. 20(3), pages 1763-1789, September.
    3. Mensendiek, Arne & Gupta, Jatinder N.D. & Herrmann, Jan, 2015. "Scheduling identical parallel machines with fixed delivery dates to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 243(2), pages 514-522.

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