Worst-case and numerical analysis of heuristic algorithms for flowshop scheduling problems with a time-dependent learning effect

In this paper, we investigate a time-dependent learning effect in a flowshop scheduling problem. We assume that the time-dependent learning effect of a job was a function of the total normal processing time of jobs scheduled before the job. The following objective functions are explored: the makespan, the total flowtime, the sum of weighted completion times, the sum of the kth power of completion times, and the maximum lateness. Some heuristic algorithms with worst-case analysis for the objective functions are given. Moreover, a polynomial algorithm is proposed for the special case with identical processing time on each machine and that with an increasing series of dominating machines, respectively. Finally, the computational results to evaluate the performance of the heuristics are provided.