Abstract: In order to enhance the efficient and orderly production of the assembly job-shops, this paper establishes a mathematical model with the objectives of minimizing makespan and total inventory time of parts to address the assembly job-shop scheduling problem considering part inventory (AJSP-PI). A multi-objective hybrid migrating birds optimization (MOHMBO) algorithm is proposed to solve the model. Considering the two-stage feature of the problem, a hybrid encoding structure is designed based on the operation sequence, and two decoding rules are proposed. In the MOHMBO algorithm, random and product aggregation rules are combined to generate the initial population, while a dual neighborhood search strategy is designed to improve the cooperative search ability and efficiency of the algorithm. Furthermore, a population competition update mechanism is proposed to enhance the diversity of the population. According to the characteristics of the problem, a variable neighborhood search operation with six kinds of neighborhood structures is introduced to further explore the globally optimal solution region to further improve solution quality. Finally, simulation experiments are conducted on generated test examples through comparing the existing multi-objective optimization algorithms with the proposed one. Experimental results verify the effectiveness of the MOHMBO algorithm in solving AJSP-PI.