To improve quality and safety and to contain costs, hospitals should optimize their processes. Therefore, they need to have a full understanding and visibility of their operations and supply chain flows. In this chapter, we combined a lean management approach using value stream mapping, with a data-driven approach using process mining applied to the surgery processes of a private hospital in Switzerland. As the sterilization process was identified as a major bottleneck, we developed a digital twin and artificial intelligence algorithms to optimize the hospital operations and supply chain management. As a result, the hospital increased the quality of its work environment, improved visibility in their processes, and developed a stronger communication channel with their teams. In addition, they could better plan schedules, which allowed the hospital to limit overtime of the operating room staff. Finally, they optimized costs and saved time in their overall sterilization process.