Minimizing the number of tardy jobs on a two-stage assembly flowshop

The objective of minimizing the number of tardy jobs is important as it is directly related to the percentage of on-time shipments, which is often used to rate managers' performance in many manufacturing environments. To the best of our knowledge, the assembly flowshop scheduling problem with this objective has not been addressed so far, and thus is addressed in this paper. Given that the problem is NP-hard, different heuristics are proposed for the problem in this paper. The proposed heuristics are genetic algorithm (GA), improved genetic algorithm (IGA), simulated annealing algorithm with three different neighborhood structures (SA-1, SA-2, SA-3), Dhouib et al.'s simulated annealing algorithm (DSA), and an improved cloud theory-based simulated annealing algorithm (CSA). The heuristics are evaluated based on extensive computational experiments and all the heuristics were run for the same computational time for a fair comparison. The experiments reveal that the overall average errors of DSA, GA, IGA, CSA, SA-1, SA-2, SA-3 were 20.53, 13.49, 11.64, 3.27, 2.81, 1.92, and 0.56, respectively. Therefore, the proposed heuristic of SA-3 reduces the error of DSA, GA, IGA, CSA, SA-1, SA-2 by about 97, 96, 95, 83, 80, and 71%, respectively. All the results are statistically confirmed.