Makespan minimization for m-machine permutation flowshop scheduling problem with learning considerations

Studies on scheduling with learning considerations have recently become important. Most studies focus on single-machine settings. However, numerous complex industrial problems can be modeled as flowshop scheduling problems. This paper thus focuses on minimizing the makespan in an m-machine permutation flowshop with learning considerations. This paper proposes a dominance theorem and a lower bound to accelerate the branch-and-bound algorithm for seeking the optimal solution. This paper also adapts four well-known existing heuristic algorithms to yield the near-optimal solutions. Eventually, the performances of all the algorithms proposed in this paper are reported for small and large job-sized problems. The computational experiments indicate that the branch-and-bound algorithm can solve problems of up to 18 jobs within a reasonable amount of time, and the heuristic algorithms are quite accurate with a mean error percentage of less than 0.1%.