With the advancement of electronic information technology and the growth of the intelligent industry, the industrial sector has undergone a shift from simplex, linear, and vertical chains to complex, multi-level, and multi-dimensional networked industrial chains. In order to enhance energy efficiency in multiplex networked industrial chains under time-of-use price, a coarse time granularity task scheduling approach has been adopted. This approach adjusts the distribution of electricity supply based on task deadlines, dividing it into longer periods to facilitate batch access to task information. However, traditional simplex-network task assignment optimization methods are unable to achieve a globally optimal solution for cross-layer links in multiplex networked industrial chains. Existing solutions struggle to balance execution costs and completion efficiency in time-of-use price scenarios. Therefore, this paper presents a mixed-integer linear programming model for solving the problem scenario and two algorithms: an exact algorithm based on the branch-and-bound method and a multi-objective heuristic algorithm based on cross-layer policy propagation. These algorithms are designed to adapt to small-scale and large-scale problem scenarios under coarse time granularity. Through extensive simulation experiments and theoretical analysis, the proposed methods effectively optimize the energy and time costs associated with the task execution.