A flowshop scheduling algorithm to minimize total weighted completion time with m machines

We consider the problem of minimizing the total weighted completion time in a flowshop. We present a heuristic algorithm and show its worst-case bound. For m=2, if jobs have agreeable weights i.e. where pi<pj implies wi=wj,(i,j=1, 2,…n), the worst-case bound is 2β/(α+β), where α and β denote the minimum and maximum processing time of all operations. Furthermore, we analyze two special cases for m=2, and polynomial algorithms are given.