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On the asymptotic optimality of algorithms for the flow shop problem with release dates

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  • Hui Liu
  • Maurice Queyranne
  • David Simchi‐Levi

Abstract

We consider the nonpermutation flow shop problem with release dates, with the objective of minimizing the sum of the weighted completion times on the final machine. Since the problem is NP‐hard, we focus on the analysis of the performance of several approximation algorithms, all of which are related to the classical Weighted Shortest Processing Time Among Available Jobs heuristic. In particular, we perform a probabilistic analysis and prove that two online heuristics and one offline heuristic are asymptotically optimal. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.

Suggested Citation

  • Hui Liu & Maurice Queyranne & David Simchi‐Levi, 2005. "On the asymptotic optimality of algorithms for the flow shop problem with release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 232-242, April.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:3:p:232-242
    DOI: 10.1002/nav.20066
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    References listed on IDEAS

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    1. DYER, Martin E. & WOLSEY, Laurence A., 1990. "Formulating the single machine sequencing problem with release dates as a mixed integer program," LIDAM Reprints CORE 878, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. E. DYER, Martin & WOLSEY, Laurence A., 1990. "Formulating the single machine sequencing problem with release dates as a mixed integer program," LIDAM Reprints CORE 917, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Philip Kaminsky & David Simchi-Levi, 2001. "The Asymptotic Optimality of the SPT Rule for the Flow Shop Mean Completion Time Problem," Operations Research, INFORMS, vol. 49(2), pages 293-304, April.
    4. Leslie A. Hall & Andreas S. Schulz & David B. Shmoys & Joel Wein, 1997. "Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 513-544, August.
    5. Pedro G. Gazmuri, 1985. "Probabilistic Analysis of a Machine Scheduling Problem," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 328-339, May.
    6. Philip Kaminsky & David Simchi-Levi, 1998. "Probabilistic Analysis and Practical Algorithms for the Flow Shop Weighted Completion Time Problem," Operations Research, INFORMS, vol. 46(6), pages 872-882, December.
    7. Marc E. Posner, 1988. "The Deadline Constrained Weighted Completion Time Problem: Analysis of a Heuristic," Operations Research, INFORMS, vol. 36(5), pages 742-746, October.
    8. Cathy H. Xia & George J. Shanthikumar & Peter W. Glynn, 2000. "On the Asymptotic Optimality of the SPT Rule for the Flow Shop Average Completion Time Problem," Operations Research, INFORMS, vol. 48(4), pages 615-622, August.
    9. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    10. W. L. Eastman & S. Even & I. M. Isaacs, 1964. "Bounds for the Optimal Scheduling of n Jobs on m Processors," Management Science, INFORMS, vol. 11(2), pages 268-279, November.
    11. 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.
    12. Leslie A. Hall, 1994. "A Polynomial Approximation Scheme for a Constrained Flow-Shop Scheduling Problem," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 68-85, February.
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    Cited by:

    1. Manzhan Gu & Xiwen Lu, 2011. "Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines," Annals of Operations Research, Springer, vol. 191(1), pages 97-113, November.
    2. Patrick Jaillet & Michael R. Wagner, 2008. "Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses," Operations Research, INFORMS, vol. 56(3), pages 745-757, June.

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