No-wait flow shop scheduling refers to continuous flow of jobs through different machines. The job once started should have the continuous processing through the machines without wait. This situation occurs when there is a lack of an intermediate storage between the processing of jobs on two consecutive machines. The problem of no-wait with the objective of minimizing makespan in flow shop scheduling is NP-hard; therefore the heuristic algorithms are the key to solve the problem with optimal solution or to approach nearer to optimal solution in simple manner. The paper describes two heuristics, one constructive and an improvement heuristic algorithm obtained by modifying the constructive one for sequencing n-jobs through m-machines in a flow shop under no-wait constraint with the objective of minimizing makespan. The efficiency of the proposed heuristic algorithms is tested on 120 Taillard's benchmark problems found in the literature against the NEH under no-wait and the MNEH heuristic for no-wait flow shop problem. The improvement heuristic outperforms all heuristics on the Taillard's instances by improving the results of NEH by 27.85%, MNEH by 22.56% and that of the proposed constructive heuristic algorithm by 24.68%. To explain the computational process of the proposed algorithm, numerical illustrations are also given in the paper. Statistical tests of significance are done in order to draw the conclusions.
Sequence-dependent setup time is the most complicated case of setup time of jobs on machines in shop scheduling. The operational cost of machines is related to the setup time required for preparation of jobs on machines. The objective is to minimize operational cost of machines subject to minimum total elapsed time of jobs for two stage flow shop problem. The setups on both the machines for jobs are considered to be sequence-dependent. The machines having different traits processing for different jobs are attached with probabilities. In addition to this, the problem also takes the effect of breakdown interval during the operation of jobs *on total elapsed time and hence on the operational cost. To solve the problem an algorithm is proposed and a numerical example is given to substantiate the algorithm.
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