Title

An FPTAS for the Parallel Two-Stage Flowshop Problem

Document Type

Article

Publication Date

1-2-2017

Publication Title

Theoretical Computer Science

DOI

10.1016/j.tcs.2016.04.046

ISSN

0304-3975

Abstract

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.

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