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Minimizing weighted mean absolute deviation of flow times in single machine systems

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  • Y. P. Aneja
  • S. N. Kabadi
  • A. Nagar

Abstract

We discuss the problem of scheduling several jobs on a single machine with the objective of minimizing the weighted mean absolute deviation of flow times around the weighted mean flow time. We first show that the optimal schedule is W‐shaped. For the unweighted case, we show that all optimal schedules are V‐shaped. This characterization enables us to show that the problem is NP‐hard. We then provide a pseudopolynomial algorithm for the unweighted problem. Finally, we consider three heuristic algorithms for the unweighted problem and report computational experience with these algorithms. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 297–311, 1998

Suggested Citation

  • Y. P. Aneja & S. N. Kabadi & A. Nagar, 1998. "Minimizing weighted mean absolute deviation of flow times in single machine systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 297-311, April.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:3:p:297-311
    DOI: 10.1002/(SICI)1520-6750(199804)45:33.0.CO;2-2
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    1. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1992. "On the Minimization of Completion Time Variance with a Bicriteria Extension," Operations Research, INFORMS, vol. 40(6), pages 1148-1155, December.
    2. John J. Kanet, 1981. "Minimizing the average deviation of job completion times about a common due date," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(4), pages 643-651, December.
    3. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
    4. Vina Vani & M. Raghavachari, 1987. "Deterministic and Random Single Machine Sequencing with Variance Minimization," Operations Research, INFORMS, vol. 35(1), pages 111-120, February.
    5. Gupta, Mahesh C. & Gupta, Yash P. & Kumar, Anup, 1993. "Minimizing flow time variance in a single machine system using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 70(3), pages 289-303, November.
    6. Samuel Eilon & I. G. Chowdhury, 1977. "Minimising Waiting Time Variance in the Single Machine Problem," Management Science, INFORMS, vol. 23(6), pages 567-575, February.
    7. John J. Kanet, 1981. "Minimizing Variation of Flow Time in Single Machine Systems," Management Science, INFORMS, vol. 27(12), pages 1453-1459, December.
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    Cited by:

    1. Gur Mosheiov, 2000. "Minimizing mean absolute deviation of job completion times from the mean completion time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 657-668, December.

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