Re-Entrant Flowshop Scheduling With Learning Considerations to Minimize The Makespan

In the more recent days, topics of scheduling reentrant flowshop settings and scheduling models with learning consideration have received growing attention separately in research areas. However, scheduling with both the learning and re-entrant concept is relatively unexplored. Motivated by this limitation, this paper considers re-entrant permutation flowshop scheduling of jobs associated with a sum-of-processing-times-based learning function to minimize the makespan. Because the same problem without learning or re-entrant has been proved NP-hard, we thus propose four heuristics and a simulated annealing (SA) to search for approximate solutions. In the first stage, Johnson's rule (JH) combined with four local search methods, which are namely the NEH method, pairwise interchange (PI), backward-shifted re-insertion (BACK), and forward-shifted re-insertion (FOR), is tackled in this problem. They are referred to the four heuristics as JH + NEH, JH + PI, JH + BACK, and JH + FOR, respectively. In the second stage, a simulated annealing algorithm seeded with four good different initials obtained from the first stage is provided for finding a good quality of solutions. Finally, the experimental results are tested to assess the performances of all the proposed algorithms as job size changes or machine number or learning effect or the number of re-entrant time.