Two-machine flowshop scheduling with a truncated learning function to minimize the makespan

Scheduling with learning effects has continued to attract the attention of scheduling researchers. However, the majority of the research on this topic has been focused on the single-machine setting. Moreover, under the commonly adopted learning model in scheduling, the actual processing time of a job drops to zero precipitously as the number of jobs increases, which is at odds with reality. To address these issues, we study a two-machine flowshop scheduling problem with a truncated learning function in which the actual processing time of a job is a function of the job's position in a schedule and the learning truncation parameter. The objective is to minimize the makespan. We propose a branch-and-bound and three crossover-based genetic algorithms (GAs) to find the optimal and approximate solutions, respectively, for the problem. We perform extensive computational experiments to evaluate the performance of all the proposed algorithms under different experimental conditions. The results show that the GAs perform quite well in terms of both efficiency and solution quality.