Worst case analysis of a new lower bound for flow shop weighted completion time problem

Abstract

For the m-machine Flow Shop Weighted Completion Time problem, a New Lower Bound (NLB) is derived to improve the original lower bound which was given by Kaminsky and Simchi-Levi. 1 ) For the case of arbitrary weight, the NLB is asymptotically equivalent to the optimality solution, as the total number of jobs goes to infinity. Specially, when the processing times of jobs are all equal, the NLB is just the optimal solution. 2) For the case of equal-weight, a tight worst case performance ratio of the optimal solution to the NLB is obtained. At the end of the paper, computational results show the effectiveness of NLB on a set of random test problems. © Springer-Verlag Berlin Heidelberg 2007.