Scheduling with job-splitting considering learning and the vital-few law

This research, which is motivated by real cases in labor-intensive industries where learning effects and the vital-few law take place, integrates learning and job splitting in parallel machine scheduling problems to minimize the makespan. We propose the lower bound of the problem and a job-splitting algorithm corresponding to the lower bound. Subsequently, a heuristic called SLMR is proposed based on the job-splitting algorithm with a proven worst case ratio. Furthermore, a branch-and-bound algorithm, which can obtain optimal solutions for very small problems, and a hybrid differential evolution algorithm are proposed, which can not only solve the problem, but also serve as a benchmark to evaluate the solution quality of the heuristic SLMR. The performance of the heuristic on a large number of randomly generated instances is evaluated. Results show that the proposed heuristic has good solution quality and calculation efficiency.