Volume 51, Number 4, October-December 2017
|Page(s)||1177 - 1188|
|Published online||24 November 2017|
Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines∗
1 Université de Lorraine, LCOMS EA 7306, 57000, Metz, France.
imed.kacem@ univ-lorraine.fr; myriam.sahnoune@ univ-lorraine.fr
2 Universität des Saarlandes, ORBI, Sarbrucken, Germany.
Received: 13 September 2016
Accepted: 26 May 2017
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 T1 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.
Mathematics Subject Classification: 90C59 / 90C39 / 90B35
Key words: Scheduling / parallel machine / approximation
© EDP Sciences, ROADEF, SMAI 2017
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