Driven by technological innovation and modern industrial transformation, the Industrial Internet of Things (IIoT) has emerged as a pivotal force in promoting the new intelligent manufacturing production paradigm. Within the paradigm, production tasks generated from heterogeneous manufacturing devices (MDs) possess intricate dependency relationships, encompassing internal dependencies (IDs) based on directed acyclic graphs (DAGs) and external dependencies (EDs) among MDs. Therefore, accurately characterizing such dependencies is crucial for reflecting the realities of modern industrial production. However, there is currently a lack of precise representations of the dependencies, as existing studies typically focus solely on IDs, failing to present the EDs that interconnect different MDs. To bridge this gap, this paper innovatively designs the multi-coupled DAGs model capable of accommodating various task dependency relationships. Moreover, by considering the aspects of dependent task offloading and transmission power allocation for data in EDs, a joint optimization problem is formulated with the objective of minimizing the system’s Energy-Time Cost (ETC). Finally, to solve this problem, we design the proximal policy optimization (PPO) based multi-coupled directed acyclic graphs for resource allocation and tasks offloading (MDRAO) algorithm. Simulation results indicate that the MDRAO algorithm outperforms its counterparts in terms of convergence performance and adaptability across various scenarios.