Algorithms with performance guarantees for flow shops with regular objective functions

We consider flow-shop scheduling problems with regular (nondecreasing) objective functions such as the minimization of makespan in the presence of arbitrary precedence constraints, the weighted sum of job completion times in the presence of series-parallel precedence constraints, the discounted total weighted completion time, and the sum of the quadratic job completion times. We present algorithms with tight worst-case performance bounds for all of these problems by utilizing the optimal permutations for the corresponding single-machine problems. We also investigate the asymptotic optimality of our algorithms.

Acknowledgements

We would like to thank the Associate Editor and two anonymous referees for their constructive criticism that helped us improve an earlier version of this paper, and also Referee 1 for supplying the NP-hardness proof for the Fm‖∑ _{j = 1} ⁿ (1−e ^{−rC _j} )/r and Fm‖∑ _{j = 1} ⁿ C _j ² problems.