NSGA-II simheuristic to solve a multi-objective flexible flow shop problem under stochastic machine breakdowns

This study proposes a simheuristic that hybridizes NSGA-II with Monte Carlo simulation to address a stochastic flexible flow shop problem featuring stochastic machine breakdowns. In real-world scenarios, machine breakdowns frequently occur, resulting in negative impacts such as time loss, late deliveries, decreased productivity, and order accumulation. Therefore, this study considers the times between failures and times to repair as stochastic parameters. Multiple objectives are concurrently addressed, including expected makespan, expected tardy jobs, and the standard deviation of tardy jobs. A mathematical model was formulated for the deterministic version of the problem and separately solved for the minimization of tardy jobs and the minimization of makespan in small instances. Subsequently, the proposed simheuristic was executed for both small and large instances. The results demonstrate that the NSGA-II simheuristic enhances outcomes across all objective functions compared to the simulation of optimal solutions provided by the mathematical models in small instances, yielding average GAPs of -16.64%, - 21.87%, and -53.33% for expected tardy jobs, expected makespan, and standard deviation of tardy jobs, respectively. Furthermore, the simheuristic outperforms the simulation of solutions given by seven dispatching rules, showcasing average improvements of 48.01%, 48.18%, and 95.63% for the same objectives, respectively.