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_i ≤ p_j implies w_i ≥ w_j, (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. For some special cases, the polynomial algorithms are given.