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.

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 T 1 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.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2017044
Classification : 90C59, 90C39, 90B35
Mots clés : Scheduling, parallel machine, approximation
Kacem, Imed 1 ; Sahnoune, Myriam 1 ; Schmidt, Günter 2

1 Université de Lorraine, LCOMS EA 7306, 57000, Metz, France.
2 Universität des Saarlandes, ORBI, Sarbrucken, Germany.
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     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},
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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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