Worst case analysis of flow shop scheduling problems with a time-dependent learning effect

In this paper we consider flow shop scheduling problems with a time-dependent learning effect. The time-dependent learning effect of a job on a machine is assumed to be a function of the total normal processing time of the jobs scheduled in front of the job on the machine. The objective is to minimize one of the five regular performance criteria namely, the total completion time, the makespan, the total weighted completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times. We present heuristic algorithms by using the optimal permutations for the special cases of the corresponding single machine scheduling problems. We also analyze the worst-case bound of the proposed heuristic algorithms.