The collaboration and interaction of multiple robots have become integral aspects of smart manufacturing. Effective planning and management play a crucial role in achieving energy savings and minimising overall costs. This paper addresses the real-time Dynamic Multiple Sources to Single Destination (DMS-SD) navigation problem, particularly with a material distribution case for multiple intelligent robots in smart manufacturing. Enumerated solutions, such as in \cite{xiao2022efficient}, tackle the problem by generating as many optimal or near-optimal solutions as possible but do not learn patterns from the previous experience, whereas the method in \cite{xiao2023collaborative} only uses limited information from the earlier trajectories. Consequently, these methods may take a considerable amount of time to compute results on large maps, rendering real-time operations impractical. To overcome this challenge, we propose a lightweight Deep Reinforcement Learning (DRL) method to address the DMS-SD problem. The proposed DRL method can be efficiently trained and rapidly converges to the optimal solution using the designed target-guided reward function. A well-trained DRL model significantly reduces the computation time for the next movement to a millisecond level, which improves the time up to 100 times in our experiments compared to the enumerated solutions. Moreover, the trained DRL model can be easily deployed on lightweight devices in smart manufacturing, such as Internet of Things devices and mobile phones, which only require limited computational resources.