Journal of Combinatorial Optimization

, Volume 25, Issue 1, pp 123-134

First online:

Two-stage proportionate flexible flow shop to minimize the makespan

  • Byung-Cheon ChoiAffiliated withDepartment of Business Administration, Chungnam National University
  • , Kangbok LeeAffiliated withDepartment of Supply Chain Management & Marketing Sciences, Rutgers Business School, The State University of New Jersey Email author 

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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.


Scheduling Proportionate flexible flow shop Computational complexity Approximation algorithm