Journal of Combinatorial Optimization

, Volume 37, Issue 2, pp 668–684 | Cite as

A fully polynomial time approximation scheme for scheduling on parallel identical two-stage openshops

  • Jianming Dong
  • Ruyan Jin
  • Jueliang Hu
  • Guohui LinEmail author


A two-stage openshop consists of a machine in the first stage and a machine in the second stage; a job processed on the two-stage openshop means it is processed non-preemptively by each of the two machines, in whichever order. We consider the scheduling problem at the availability of multiple parallel identical two-stage openshops, with the goal to minimize the makespan. By uncovering the important role of the critical job in the optimal schedule on a two-stage openshop, we propose to sort the jobs in the novel critical-job order, and use this order to design a pseudo-polynomial time dynamic programming exact algorithm to solve our scheduling problem with any fixed number of two-stage openshops. Afterwards, using the standard scaling technique, we develop the dynamic programming algorithm into a fully polynomial-time approximation scheme. These results improve previously proposed constant ratio approximation algorithms.


Scheduling Two-stage openshop Makespan Dynamic programming Fully polynomial-time approximation scheme 



JD is supported by the NNSF China Grant No. 11501512 and the Zhejiang Provincial Natural Science Foundation Grant No. LY18A010029; part of his work was done while visiting the University of Alberta. JH is supported by the NNSF China Grants Nos. 11271324 and 11471286; part of his work was done while visiting the University of Alberta. GL is supported by NSERC Canada and the NNSF China Grant No. 61672323.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Sci-Tech UniversityHangzhouChina
  2. 2.Department of Computing ScienceUniversity of AlbertaEdmontonCanada

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