Journal of Combinatorial Optimization

, Volume 25, Issue 1, pp 123–134

Two-stage proportionate flexible flow shop to minimize the makespan


DOI: 10.1007/s10878-011-9423-1

Cite this article as:
Choi, BC. & Lee, K. J Comb Optim (2013) 25: 123. doi:10.1007/s10878-011-9423-1


We consider a two-stage flexible flow shop problem with a single machine at one stage and m identical machines at the other stage, where the processing times of each job at both stages are identical. The objective is to minimize the makespan. We describe some optimality conditions and show that the problem is NP-hard when m is fixed. Finally, we present an approximation algorithm that has a worst-case performance ratio of \(\frac{5}{4}\) for m=2 and \(\frac{\sqrt{1+m^{2}}+1+m}{2m}\) for m≥3.


SchedulingProportionate flexible flow shopComputational complexityApproximation algorithm

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Business AdministrationChungnam National UniversityDaejeonKorea
  2. 2.Department of Supply Chain Management & Marketing Sciences, Rutgers Business SchoolThe State University of New JerseyNewarkUSA