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:https://doi.org/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 / School / Research Centre / Research Group:	Faculty of Liberal Arts & Sciences
Related URLs:	Publisher
Last Modified:	14 Oct 2016 09:14
URI:	http://gala.gre.ac.uk/id/eprint/5654

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