Flexible open shop scheduling problem to minimize makespan

•Asymptotic optimality of general dense scheduling algorithm for flexible open shop.•Design of differential evolution algorithm for flexible open shop problem.•Asymptotic optimality of list scheduling algorithm for parallel-machine problem.

This study investigates the static and dynamic versions of the flexible open shop scheduling problem with the goal of minimizing makespan. The asymptotic optimality of the general dense scheduling (GDS) algorithm is proven by the boundedness hypothesis. For large-scale problems, the GDS-based heuristic algorithms are presented to accelerate convergence. For moderate-scale problems, the differential evolution algorithm is employed to obtain high-quality solutions. A series of random experiments are conducted to demonstrate the effectiveness of the proposed algorithms.