We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.
Accepté le :
DOI : 10.1051/ro/2017044
Mots-clés : Scheduling, parallel machine, approximation
@article{RO_2017__51_4_1177_0,
author = {Kacem, Imed and Sahnoune, Myriam and Schmidt, G\"unter},
title = {Strongly {Fully} {Polynomial} {Time} {Approximation} {Scheme} for the weighted completion time minimization problem on two-parallel capacitated machines},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1177--1188},
publisher = {EDP-Sciences},
volume = {51},
number = {4},
year = {2017},
doi = {10.1051/ro/2017044},
mrnumber = {3783940},
zbl = {1395.90148},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2017044/}
}
TY - JOUR AU - Kacem, Imed AU - Sahnoune, Myriam AU - Schmidt, Günter TI - Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 1177 EP - 1188 VL - 51 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2017044/ DO - 10.1051/ro/2017044 LA - en ID - RO_2017__51_4_1177_0 ER -
%0 Journal Article %A Kacem, Imed %A Sahnoune, Myriam %A Schmidt, Günter %T Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 1177-1188 %V 51 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2017044/ %R 10.1051/ro/2017044 %G en %F RO_2017__51_4_1177_0
Kacem, Imed; Sahnoune, Myriam; Schmidt, Günter. Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1177-1188. doi : 10.1051/ro/2017044. http://www.numdam.org/articles/10.1051/ro/2017044/
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