Scheduling concerns the allocation of limited resources overtime to perform tasks to fulfill certain criterion and optimize one or several objective functions. One of the most popular models in scheduling theory is that of the flow-shop scheduling. During the last 40 years, the permutation flow-shop sequencing problem with the objective of makespan minimization has held the attraction of many researchers. This problem characterized as Fm/prmu/Cmax in the notation of Graham, involves the determination of the order of processing of n jobs on m machines. In addition, there was evidence that m-machine permutation flow-shop scheduling problem (PFSP) is strongly NP-hard for m ≥3. Due to this NP-hardness, many heuristic approaches have been proposed, this work falls within the framework of the scientific research, whose purpose is to study Cuckoo search algorithm. Also, the objective of this study is to adapt the cuckoo algorithm to a generalized permutation flow-shop problem for minimizing the total completion time, so the problem is denoted as follow: Fm | | Cmax. Simulation results are judged by the total completion time and algorithm run time for each instance processed.

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