The planning of complex logistic systems must ensure collision- and deadlock-free operation of the logistic system. Problem-specific rule-based algorithms used so far are inflexible with respect to infrastructure changes and scale poorly with systems that grow larger. This paper shows a first approach to handle logistic deadlocks with machine learning. We present a conceptual approach on how to handle logistic deadlocks with artificial neural networks. The paper also provides a technical implementation with a single agent approach based on reinforcement learning with deep Q-networks. A discrete event simulation of an automated guided vehicle system is used as the learning environment. The first results show that artificial neural networks can learn to handle deadlock capable logistic systems with low complexity.