Optimization of Energy-Constrained Task Assignment and Resource Allocation Under End–Edge–Cloud Collaborative Framework

The rise of the Industrial Internet of Things (IIoT) has led to latency-sensitive, computation-intensive applications. While cloud computing provides abundant resources, communication latency and congestion limit real-time performance. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">end–edge–cloud</i> collaborative framework mitigates these challenges by incorporating edge computing. However, task heterogeneity and limited resource capacity on the edge necessitate efficient joint task assignment and resource allocation. To address this, we formulate a fractional integer programming (FIP) model to minimize task completion latency while adhering to a global energy constraint at the edge layer. By deriving an analytical solution for resource allocation, the FIP is transformed into an NP-hard integer quadratic programming (IQP) problem. To efficiently solve large-scale instances, we develop an enhanced Lagrangian relaxation algorithm that uses state-reduction dynamic programming for subproblems and list scheduling to obtain tight upper bounds. Experiments show that our approach matches the state-of-the-art solver Gurobi on small instances and outperforms it on large ones, maintaining a dual gap within 4%. It also delivers higher quality solutions and lower latency compared with the deep reinforcement learning (DRL) approach. Without energy constraints, it improves the objective and accelerates computation by orders of magnitude compared with existing baselines. Comprehensive evaluation confirms the method’s effectiveness.