Citation
Single Machine and Parallel Machine Scheduling Problems with a Common Due Date to Minimize Total Weighted Tardiness. In proceedings of the 3rd Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2007), 28 -31 August 2007, Paris, France, pages 498-505, 2007.
Paper
Abstract
This paper deals with a common due date parallel machines scheduling problem in which each job has a different tardiness penalty. The objective is to minimize the total weighted tardiness. The scheduling problem of minimizing the total weighted tardiness with a common due date on a single machine is known to be ordinary NP-hard. This is also the case for problem Pm|di = d|PwiTi. A new dynamic programming algorithm is proposed to solve the 1|d_i = d|SUM(w_1*T_i) scheduling problem and a fully polynomial time approximation scheme (FPTAS) is deduced from this algorithm. We show that the complexity of this FPTAS is better than existing one. These results are generalized to the parallel machines scheduling case.
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Bibtex
@INPROCEEDINGS{2007-498-505-P, author = {N. Huynh Tuong and A. Soukhal and J-C. Billaut},
title = {Single Machine and Parallel Machine Scheduling Problems with a Common Due Date to Minimize Total Weighted Tardiness},
booktitle = {In proceedings of the 3rd Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2007), 28 -31 August 2007, Paris, France},
year = {2007},
editor = {P. Baptiste and G. Kendall and A. Munier-Kordon and F. Sourd},
pages = {498--505},
note = {Paper},
abstract = {This paper deals with a common due date parallel machines scheduling problem in which each job has a different tardiness penalty. The objective is to minimize the total weighted tardiness. The scheduling problem of minimizing the total weighted tardiness with a common due date on a single machine is known to be ordinary NP-hard. This is also the case for problem Pm|di = d|PwiTi. A new dynamic programming algorithm is proposed to solve the 1|d_i = d|SUM(w_1*T_i) scheduling problem and a fully polynomial time approximation scheme (FPTAS) is deduced from this algorithm. We show that the complexity of this FPTAS is better than existing one. These results are generalized to the parallel machines scheduling case.},
owner = {user},
timestamp = {2012.05.22},
webpdf = {2007-498-505-P.pdf} }