Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem

2011 ◽  
Vol 1 (1/2) ◽  
pp. 32 ◽  
Author(s):  
Imed Kacem ◽  
Yann Lanuel ◽  
Myriam Sahnoune
Keyword(s):  
Polynomial Time ◽  
Approximation Scheme ◽  
Scheduling Problem ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Polynomial Time Approximation

scholarly journals Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines

2017 ◽  
Vol 51 (4) ◽  
pp. 1177-1188 ◽  
Author(s):  
Imed Kacem ◽  
Myriam Sahnoune ◽  
Günter Schmidt
Keyword(s):  
Polynomial Time ◽  
Completion Time ◽  
Approximation Scheme ◽  
Dynamic Programming Algorithm ◽  
Scheduling Problem ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Time Minimization ◽  
Weighted Completion Time ◽  
Polynomial Time Approximation

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.

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