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Bounding strategies for obtaining a lower bound for N-job and M-machine flowshop scheduling problem with objective of minimising the total flowtime of jobs

Author

Listed:
  • S. Saravana Kumar
  • C. Rajendran
  • Rainer Leisten

Abstract

In this paper, bounding strategies for determining a lower bound on the completion time of a job sequenced in each position in the permutation sequence on each machine in permutation flowshop scheduling problem with minimisation of total flowtime of jobs as objective are discussed. Basically, the bounding strategies are machine-based bounding strategies used for determining the lower bound on total flowtime of jobs for all the small-sized and large-sized benchmark flowshop scheduling problem instances proposed by Vallada et al. (2015). The lower bound matrix can be pruned as tightening constraints into the mixed integer linear programming (MILP) model with objective of minimisation of total flowtime of jobs. Since the flowshop scheduling problem with total flowtime objective is difficult, two kinds of linear programming (LP) relaxation methods are used for determining an LP-based lower bound on total flowtime of jobs for some benchmark problem instances proposed by Vallada et al. (2015).

Suggested Citation

  • S. Saravana Kumar & C. Rajendran & Rainer Leisten, 2021. "Bounding strategies for obtaining a lower bound for N-job and M-machine flowshop scheduling problem with objective of minimising the total flowtime of jobs," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 41(2), pages 244-269.
    • Handle: RePEc:ids:ijores:v:41:y:2021:i:2:p:244-269
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