Systems where both machines and workers are treated as constraints are termed Dual-Resource Constrained (DRC) systems. In the last few decades, DRC scheduling has attracted much attention from researchers. This paper addresses the Dual- Resource Constrained Flexible Job-Shop Scheduling Problem (DRCFJSP) to minimize makespan. This problem is NP-hard and mainly includes three sub-problems: (1) assigning each operation to a machine out of a set of compatible machines, (2) determining a worker among a set of skilled workers for operating each operation on the selected machine, and (3) sequencing the operations on the machines considering workers in order to optimize the performance measure. This paper presents two meta-heuristic algorithms, namely Simulated Annealing (SA), and Vibration Damping Optimization (VDO), to solve the DRCFJSP. The proposed algorithms make use of various neighborhood structures to search in the solution space. The Taguchi experimental design method as an optimization technique is employed to tune different parameters and operators of the presented algorithms. Numerical experiments with randomly generated test problems are used to evaluate performance of the developed algorithms. A lower bound is used to obtain the minimum value of makespan for the test problems. The computational study confirms the proper quality of the results of the proposed algorithms.