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

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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 \(1 ||\varSigma {w}_{j} C_{j}\) where the objective of total weighted completion time admits WSPT (i.e., scheduling jobs in non-decreasing order of \(p_{j}/w_{j}\)). We provide new proofs by induction for the optimality of WSPT as well as for SPT in the unweighted case.

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Authors and Affiliations

  1. Department of MIS/OM/DSC, University of Dayton, 300 College Park, Dayton, OH, 45419-2130, USA

    J. J. Kanet & C. E. Wells

Authors
  1. J. J. Kanet
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  2. C. E. Wells
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Correspondence to J. J. Kanet.

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Kanet, J.J., Wells, C.E. An examination of job interchange relationships and induction-based proofs in single machine scheduling. Ann Oper Res 253, 345–351 (2017). https://doi.org/10.1007/s10479-016-2289-y

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  • DOI: https://doi.org/10.1007/s10479-016-2289-y

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