Worst-case analysis for flow shop scheduling with a learning effect

We consider flow shop scheduling problems with a learning effect. In this model the processing times of jobs are defined as functions of their positions in a permutation. The objective is to minimize one of the three regular performance criteria, namely, the total weighted completion time, the discounted total weighted completion time, and the sum of the quadratic job completion times. We present algorithms by using the optimal permutations for the corresponding single machine scheduling problems. We also analyze the worst-case bound of our algorithms.