Abstract
In the paper we consider an approximate O(n log n) time solution of theproblem of a single machine scheduling with time dependentprocessing times, where α j ≥ 0.The main result of the paper is that in view of the inequality‖C‖1 ≤ ω(n,r)‖C‖ r , where‖C‖ r = (n + l)1-1/r and1 ≤ r ≤ +∞, the solution of the ‖C‖1— problem with the actuallyrecognized O(2n) complexity ((1991)) can beapproximated in terms of the l p —norm-based criteria ‖C‖ r merely with the complexity O(n log n), where 1 < r 1 ≤r ≤ +∞and r 1 is large enough. Relations to some more general problems are also indicated.
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The research of the author has beenpartially supported by KBN (Polish Scientific Committee)grant no. 8T 11A 01618.
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Gawiejnowicz, S., Kurc, W., Pankowska, L., Suwalski, C. (2001). Approximate Solution of a Time-dependent Scheduling Problem for l p -norm-based Criteria. In: Fleischmann, B., Lasch, R., Derigs, U., Domschke, W., Rieder, U. (eds) Operations Research Proceedings. Operations Research Proceedings, vol 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56656-1_59
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DOI: https://doi.org/10.1007/978-3-642-56656-1_59
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