As an integral part of production planning control, order release management is critical to enhance the competitiveness and production efficiency of companies. Previous literature shows limited application of optimization-based models in assembly job shops, primarily due to the intricate nature of product structures and assembly operations. Therefore, based on the idea of the allocated clearing function (ACF) model, we introduce material flow constraints and complex assembly structure constraints during the assembly stage, proposing the assembly job shop allocated clearing function (AACF) model. The performance of the AACF model and the rule-based mechanisms in terms of cost and timing measures are compared through experiments containing 6 factors and 96 scenarios. The results show that the AACF model performs better in terms of cost management, service level and order due date deviation. In addition, a sensitivity analysis of the objective function parameters is performed to confirm the robustness of the AACF model. Finally, a case application in a real assembly shop illustrates the feasibility and validity of the proposed AACF model.