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

J. J. Kanet () and C. E. Wells
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J. J. Kanet: University of Dayton
C. E. Wells: University of Dayton

Annals of Operations Research, 2017, vol. 253, issue 1, No 15, 345-351

Abstract: 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.

Keywords: Single-machine scheduling; Permutation scheduling; Job interchange relation; Weighted processing time (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10479-016-2289-y

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