An FPTAS for the Parallel Two-Stage Flowshop Problem
Theoretical Computer Science
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.
Dong, Jianming, Weitian Tong, Taibo Luo, Xueshi Wang, Jueliang Hu, Yinfeng Xu, Guohui Lin.
"An FPTAS for the Parallel Two-Stage Flowshop Problem."
Theoretical Computer Science, 657 (A): 64-72.
doi: 10.1016/j.tcs.2016.04.046 source: https://www.sciencedirect.com/science/article/pii/S0304397516302250?via%3Dihub