Abstract
We consider the proportionate flow shop total tardiness problem and show how to implement Lawler's (1977) pseudo-polynomial dynamic programming (DP) algorithm for the single-machine total tardiness problem to the multi-machine environment of proportionate flow shop. We also present solvable special cases including one with small/big jobs that has not been considered for the corresponding single-machine problem. We then convert the DP algorithm for the proportionate flow shop to a fully polynomial time approximation scheme (FPTAS). Finally, we show by a counterexample that Pinedo's (2002, p. 140) statement that “the elimination criteria for the single-machine total weighted tardiness problem also apply to the proportionate flow shop total weighted tardiness problem” does not always hold and present an appropriately revised statement.
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