Complaints about finished products are a major challenge for companies in the medical technology industry, where product quality is directly related to public health and therefore strictly regulated. In this paper, we examine how available data can be used to provide automated support to the complaint handling processes in the medical technology companies. We identify the automation potentials in the 8D reference process for complaint management and discuss their organizational and technical challenges. Using data from a large manufacturer of medical products, we show how partial process automation can be achieved in practice by designing, implementing, and evaluating a deep learning-based prototype for automatically suggesting a likely error code for future complaints, given their textual description. Our approach is able to assign the correct error code for more than 75% of all cases and outperforms the conventional classification approaches used as a baseline comparison. Our results show that partial automation of a complaint management process by means of deep learning can be achieved in practice.