An fptas for the weighted number of tardy jobs minimization on a single machine with deteriorating jobs

Chuanli Zhao

doi:10.3934/jimo.2016033

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2017, Volume 13, Issue 2: 587-593. Doi: 10.3934/jimo.2016033

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An fptas for the weighted number of tardy jobs minimization on a single machine with deteriorating jobs

Chuanli Zhao^,

School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, Liaoning 110034, China

* Corresponding author
* Corresponding author

Received: September 2015

Revised: December 2015

Published: August 2017

This paper was supported by Science and Research Project Foundation of Liaoning Province Education Department (L2014433).

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Abstract

We consider a single machine scheduling problem in which the processing time of a job is a nondecreasing function of its starting time. The jobs have a common due date. The objective is to minimize the weighted number of tardy jobs. The problem is NP-hard. We present a pseudo-polynomial dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS).

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Mathematics Subject Classification: Primary: 90B35; Secondary: 90C26.

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