, Volume 25, Issue 1, pp 123-134
Date: 30 Nov 2011

Two-stage proportionate flexible flow shop to minimize the makespan

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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.