Journal of Combinatorial Optimization

, Volume 25, Issue 1, pp 123–134

Two-stage proportionate flexible flow shop to minimize the makespan

Authors

  • Byung-Cheon Choi
    • Department of Business AdministrationChungnam National University
    • Department of Supply Chain Management & Marketing Sciences, Rutgers Business SchoolThe State University of New Jersey
Article

DOI: 10.1007/s10878-011-9423-1

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

Abstract

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.

Keywords

SchedulingProportionate flexible flow shopComputational complexityApproximation algorithm

Copyright information

© Springer Science+Business Media, LLC 2011