No-wait and separate setup three-machine flowshop with total completion time criterion

This paper considers the three-machine no-wait flowshop problem with the objective of minimizing total completion time where setup times are considered as separate from processing times and sequence independent. We present optimal solutions for certain cases, and a dominance relation for the general case. We also develop and evaluate five heuristic algorithms for small and large numbers of jobs. Computational experience for up to 100 jobs shows that the proposed heuristics are quite effective and their performance does not depend on the number of jobs. The computational experience has been conducted for the uniform processing time distributions of U(1, 10) and U(1, 100). The best heuristic gives an overall average error of 0.47% for U(1, 10) and it gives an overall average error of 1.23% for U(1, 100).