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Minimizing total weighted earliness-tardiness on a single machine around a small common due date: an FPTAS using quadratic knapsack

Minimizing total weighted earliness-tardiness on a single machine around a small common due date: an FPTAS using quadratic knapsack

Kellerer, Hans and Strusevich, Vitaly A. (2010) Minimizing total weighted earliness-tardiness on a single machine around a small common due date: an FPTAS using quadratic knapsack. International Journal of Foundations of Computer Science (IJFCS), 21 (3). pp. 357-383. ISSN 0129-0541 (Print), 1793-6373 (Online) (doi:10.1142/S0129054110007301)

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Abstract

We design a fully polynomial-time approximation scheme (FPTAS) for a single machine scheduling problem to minimize the total weighted earliness and tardiness with respect to a common restrictive due date. Notice that for this problem no constant-ratio approximation algorithm has been known so far. Our approach is based on adopting an FPTAS for a special version of the knapsack problem to minimize a convex quadratic non-separable function. For the continuous relaxation of such a knapsack problem we give an algorithm of a quadratic time complexity. The running time of the resulting FPTAS is strongly polynomial.

Item Type: Article
Uncontrolled Keywords: quadratic knapsack, single machine scheduling, earliness-tardiness, FPTAS
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Related URLs:
Last Modified: 14 Oct 2016 09:14
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/5654

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