Multi-Stage assembly flow shop with setup time and release time

This article addresses multi-stage assembly flow shop for the first time. We propose several industrial applications of this system in which the opening stage has m parallel machines and the following stages (e.g. assembly, transportation, painting, packaging, etc.) complete and prepare products for delivery. We develop a mixed binary linear optimization model and a constraint-free mathematical presentation for this problem. We explore performance measures of makespan and total completion time and derive polynomial optimal solutions for special cases that are likely to occur in industry. We also propose lower bounds as well as nine efficient heuristics for solving the problem with the objective of minimizing makespan. The results reveal that the proposed lower bounds is tight enough. Moreover, the optimization models and derived polynomial algorithms can be applied to assembly flow shops without setup or release time. Finally, we implement General Variable Neighborhood Search (GVNS) and Grey Wolf Optimizer to improve the heuristic solutions. Comparison of employed algorithms on randomly generated instances indicates that GVNS outperforms other heuristics. The performance of proposed heuristics and meta-heuristics are confirmed with detailed statistical analysis.