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This research aims to develop a CUDA accelerated NEH algorithm for the permutative flowshop scheduling problem with makespan criterion. NEH has been shown in the literature as the best constructive heuristic for this particular problem. The CUDA based NEH aims to speed up the processing time by utilising the GPU cores for parallel evaluation. In order to show the versatility and scalability of the CUDA based NEH, four new higher dimensional Taillard sets are generated. The experiments are conducted on the CPU and GPU and pairwise compared. Percentage relative difference and paired t-test both confirm that the GPU based NEH significantly improves on the execution time compared to the sequential CPU version for all the high dimensional problem instances.