Total completion time minimization in a 2-stage differentiation flowshop with fixed sequences per job type

This paper addresses the total completion time minimization in a two-stage differentiation flowshop where the sequences of jobs per type are predetermined. The two-stage differentiation flowshop consists of a stage-1 common machine and m stage-2 parallel dedicated machines. The goal is to determine an optimal interleaved processing sequence of all jobs at the first stage. We propose an O(m2∏k=1mnkm+1) dynamic programming algorithm, where nk is the number of type-k jobs. The running time is polynomial when m is constant.