This paper considers the m-machine flow shop scheduling problem with the no-wait constraint to minimize total completion time which is the typical model in steel production. First, the asymptotic optimality of the Shortest Processing Time (SPT) first rule is proven for this problem. To further evaluate the performance of the algorithm, a new lower bound with performance guarantee is designed. At the end of the paper, numerical simulations show the effectiveness of the proposed algorithm and lower bound.
"Optimal Research and Numerical Simulation for Scheduling No-Wait Flow Shop in Steel Production." J. Appl. Math. 2013 1 - 5, 2013. https://doi.org/10.1155/2013/498282