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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 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. For some special cases, the polynomial algorithms are given.