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Lower bounds for single‐machine scheduling problems

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  • Reza H. Ahmadi
  • Uttarayan Bagchi

Abstract

This article addresses deterministic, nonpreemptive scheduling of n jobs with unequal release times on a single machine to minimize the sum of job completion times. This problem is known to be NP‐hard. The article compares six available lower bounds in the literature and shows that the lower bound based on the optimal solution to the preemptive version of the problem is the dominant lower bound.

Suggested Citation

  • Reza H. Ahmadi & Uttarayan Bagchi, 1990. "Lower bounds for single‐machine scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(6), pages 967-979, December.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:6:p:967-979
    DOI: 10.1002/1520-6750(199012)37:63.0.CO;2-K
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    References listed on IDEAS

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    1. Potts, C. N. & Van Wassenhove, L. N., 1983. "An algorithm for single machine sequencing with deadlines to minimize total weighted completion time," European Journal of Operational Research, Elsevier, vol. 12(4), pages 379-387, April.
    2. Marc E. Posner, 1985. "Minimizing Weighted Completion Times with Deadlines," Operations Research, INFORMS, vol. 33(3), pages 562-574, June.
    3. Lucio Bianco & Salvatore Ricciardelli, 1982. "Scheduling of a single machine to minimize total weighted completion time subject to release dates," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(1), pages 151-167, March.
    4. Ramesh Chandra, 1979. "On n/1/F̄ dynamic deterministic problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 537-544, September.
    5. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
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    Cited by:

    1. Chengbin Chu, 1992. "A branch‐and‐bound algorithm to minimize total flow time with unequal release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 859-875, October.

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