Industry 4.0, big data, predictive analytics, and robotics are leading to a paradigm shift on the shop floor of industrial production. However, complex, cognitive tasks are also subject of change, due to the development of artificial intelligence (AI). Smart assistants are finding their way into the world of knowledge work and require cooperation with humans. Here, trust is an essential factor that determines the success of human-AI cooperation. Within this article, an analysis within production management identifies possible antecedent variables on trust in AI and evaluates these due to interaction scenarios with AI. The results of this research are five antecedents for human trust in AI within production management. From these results, preliminary design guidelines are derived for a socially sustainable human-AI interaction in future production management systems. In the future, artificial intelligence will assist cognitive tasks in production management. In order to make good decisions, humans trust in AI has to be well calibrated. For trustful human-AI interactions, it is beneficial that humans subjectively perceive AI as capable and comprehensible and that they themselves are digitally competent.