Abstract: To address the problems that traditional methods in intelligent underground coal mine inspection have difficulty accurately characterizing task computation costs, making precise offloading decisions, and achieving multi-objective optimization under resource constraints, this paper proposed a complexity modeling-based task offloading and edge resource optimization method for underground coal mine inspection. The local offloading decision layer of the inspection robot determined whether a task should be executed locally on the robot or offloaded to the edge side according to task complexity, input size, and the real-time resource status of underground Mobile Edge Computing (MEC) nodes. For pre-offloaded tasks, the multi-task MEC resource scheduling layer adopted a Weighted Satisfaction Resource Management Algorithm (WSRMA) to optimize bandwidth and computing resource allocation, and further improved the allocation effect through local search. Simulation results showed that: ① the performance differences between local computation and edge offloading for different tasks were mainly determined by computational complexity and data volume. Tasks with high complexity and large uplink data volumes performed better with offloading only when their scale exceeded the offloading threshold, whereas lightweight tasks achieved the highest benefits from local execution in all scenarios. ② In dynamic bandwidth scenarios, the average satisfaction of WSRMA was improved by 18.85%, 29.52%, 38.21%, and 26.42% compared with the Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Random Allocation Algorithm (Random), Round-Robin Algorithm (RR), and Deep Deterministic Policy Gradient (DDPG), respectively. Under different computing power scenarios, the average satisfaction of WSRMA was improved by 21.88%, 75.15%, 36%, and 47.15%, respectively. ③ The task delay of WSRMA was controlled within 0.295-0.314 s, and the energy consumption remained stable at 0.264-0.279 J, indicating its suitability for resource-constrained underground coal mine scenarios. ④ The overall time complexity of WSRMA was much lower than that of NSGA-II and DDPG, enabling substantial system performance improvement with extremely low additional computational overhead.