A new three stage production-assembly problem is considered in this paper. To the best of our knowledge, considering parallel machines in the third stage, identical parallel factories including the three stage production-assembly system and identical parallel factories with parallel machines in the third stage of the production-assembly system, has been specifically investigated in this paper. To minimize the maximum completion time (Makespan) of all jobs in the all factories, jobs assignment to factories and their processing sequence should be done properly. A Mixed Integer Linear Programming (MILP) model is presented to solve small size problem by using cplex solver. According to the problem computational complexity, large size of problem is not possible to solve using the cplex, so to solve it and to control the computational complexity, a new improved genetic algorithm (GA) is proposed by combining GA and Longest Proseccing Time (LPT) method that is called Hybrid Genetic Algorithm Longest Proseccing Time (HGALPT). The problem parameters values are determined using one-way analysis of variance (ANOVA). Finally, in order to evaluate the efficiency and effectiveness of the proposed algorithm, and to specify each parameter impact on the objective function, sensitivity analysis is performed on the problem parameters.
