Non-emergency Patient Transport Services (PTS) are provided by ambulance companies for patients who do not require urgent and emergency transport. These patients require transport to or from a health facility like a hospital, but due to clinical requirements are unable to use private or public transport. This task is performed nowadays mainly by human operators, spending a high amount of time and resources to obtain solutions that are suboptimal in most cases. To overcome this limitation, in this paper we present NURA (Non-Urgent transport Routing Algorithm), a novel algorithm aimed at ambulance route planning. In particular, NURA relies on a genetic algorithm to explore the solution space, and it includes a scheduling algorithm to generate detailed routes for ambulances. Experimental results show that NURA is able to outperform human experts in several real scenarios, reducing the time spent by patients in ambulances during non-emergency transportations, increasing ambulance usage, while saving time and money for ambulance companies.