A flowshop scheduling algorithm to minimize total weighted completion time

The paper considers the problem of minimizing total weighted completion time in a flowshop. A heuristic algorithm with worst-case bound m is given. For m = 2, if jobs have agreeable weights i.e. where p/sub i/ /spl les/ p/sub j/ implies w/sub i/ /spl ges/ w/sub j/, (i, j = 1, 2, /spl middot//spl middot//spl middot/, n). The worst-case bound is 2/spl beta///spl alpha/+/spl beta/, where /spl alpha/ and /spl beta/ denote the minimum and maximum processing time of all operations. For some special cases, the polynomial algorithms are given.