An FPTAS for the parallel two-stage flowshop problem

We consider the NP-hard m-parallel two-stage flowshop problem, abbreviated as the (m,2)-PFS problem, where we need to schedule n jobs to m parallel identical two-stage flowshops in order to minimize the makespan, i.e. the maximum completion time of all the jobs on the m flowshops. The (m,2)-PFS prob...

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Bibliographic Details
Published in:Theoretical computer science Vol. 657; pp. 64 - 72
Main Authors: Dong, Jianming, Tong, Weitian, Luo, Taibo, Wang, Xueshi, Hu, Jueliang, Xu, Yinfeng, Lin, Guohui
Format: Journal Article
Language:English
Published: Elsevier B.V 02.01.2017
Subjects:
Dynamic programming
Fully polynomial-time approximation scheme
Makespan
Multiprocessor scheduling
Two-stage flowshop scheduling
Multiprocessor scheduling
Fully polynomial-time approximation scheme
Makespan
Dynamic programming
Two-stage flowshop scheduling
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We consider the NP-hard m-parallel two-stage flowshop problem, abbreviated as the (m,2)-PFS problem, where we need to schedule n jobs to m parallel identical two-stage flowshops in order to minimize the makespan, i.e. the maximum completion time of all the jobs on the m flowshops. The (m,2)-PFS problem can be decomposed into two subproblems: to assign the n jobs to the m parallel flowshops, and for each flowshop to schedule the jobs assigned to the flowshop. We first present a pseudo-polynomial time dynamic programming algorithm to solve the (m,2)-PFS problem optimally, for any fixed m, based on an earlier idea for solving the (2,2)-PFS problem. Using the dynamic programming algorithm as a subroutine, we design a fully polynomial-time approximation scheme (FPTAS) for the (m,2)-PFS problem.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2016.04.046