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Minimizing Single-Machine Completion Time Variance

Author

Listed:
  • Jose A. Ventura

    (Department of Industrial and Manufacturing Engineering, 207 Hammond Building, The Pennsylvania State University, University Park, Pennsylvania 16802)

  • Michael X. Weng

    (Department of Industrial and Management Systems Engineering, 4202 East Fowler Avenue, University of South Florida, Tampa, Florida 33620)

Abstract

In this article the problem of minimizing the completion time variance in n-job, single-machine scheduling is considered. The release times for all jobs are assumed to be zero. A new quadratic integer programming formulation is introduced. A Lagrangian relaxation (LR) procedure is developed to find a lower bound (LB) to the optimal objective value. When the number of jobs is between 100 and 500, our computational study shows that the lower bounds obtained by the LR procedure are very close to the best known objective values. A new heuristic algorithm is also described. The first phase of the heuristic algorithm is a construction procedure whose purpose is to identify a good initial sequence. The second phase is an improvement procedure based on pairwise interchanges. The new heuristic algorithm provides improved solutions compared to the best known heuristic.

Suggested Citation

  • Jose A. Ventura & Michael X. Weng, 1995. "Minimizing Single-Machine Completion Time Variance," Management Science, INFORMS, vol. 41(9), pages 1448-1455, September.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:9:p:1448-1455
    DOI: 10.1287/mnsc.41.9.1448
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    Citations

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    Cited by:

    1. Pereira, Jordi & Vásquez, Óscar C., 2017. "The single machine weighted mean squared deviation problem," European Journal of Operational Research, Elsevier, vol. 261(2), pages 515-529.
    2. Ganesan, Viswanath Kumar & Sivakumar, Appa Iyer, 2006. "Scheduling in static jobshops for minimizing mean flowtime subject to minimum total deviation of job completion times," International Journal of Production Economics, Elsevier, vol. 103(2), pages 633-647, October.
    3. Patriksson, Michael & Strömberg, Christoffer, 2015. "Algorithms for the continuous nonlinear resource allocation problem—New implementations and numerical studies," European Journal of Operational Research, Elsevier, vol. 243(3), pages 703-722.
    4. Koulamas, Christos & Kyparisis, George J., 2023. "Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection," European Journal of Operational Research, Elsevier, vol. 305(2), pages 608-616.

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