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An examination of job interchange relationships and induction-based proofs in single machine scheduling

Author

Listed:
  • J. J. Kanet

    (University of Dayton)

  • C. E. Wells

    (University of Dayton)

Abstract

We provide a generalization of Lawler’s (Mathematical programming the state of the art. Springer, Berlin, pp 202–234, 1983) Theorem on solutions to permutation scheduling problems when the objective function admits a particular job interchange relation. We complete Lawler’s result with a straight-forward proof by induction on n, the number of jobs. A notable application is $$1 ||\varSigma {w}_{j} C_{j}$$ 1 | | Σ w j C j where the objective of total weighted completion time admits WSPT (i.e., scheduling jobs in non-decreasing order of $$p_{j}/w_{j}$$ p j / w j ). We provide new proofs by induction for the optimality of WSPT as well as for SPT in the unweighted case.

Suggested Citation

  • J. J. Kanet & C. E. Wells, 2017. "An examination of job interchange relationships and induction-based proofs in single machine scheduling," Annals of Operations Research, Springer, vol. 253(1), pages 345-351, June.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2289-y
    DOI: 10.1007/s10479-016-2289-y
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