This study presents an optimisation model for scheduling homebound vaccination in a more efficient way to address the existing workforce management challenge. We consider a home healthcare routeing challenge for people to be vaccinated at home based on limited resources. There are different types of patients that are categorised based on the services they require and should be served by appropriate workforce teams or a single medical staff, where teams are transported by rental vehicles. In this context, our goal is to minimise the total cost of transportation while considering patient requirements and workforce qualifications, as well as resource constraints and the time limit within which the vaccine must be administered. To pursue this goal, a mathematical formulation, based on the vehicle routeing dynamics is proposed, along with an algorithm to address the challenge. A case study with a Physician who administers vaccinations at home in southeastern Italy is analysed. Driving and working times are subject to uncertainty and are defined by empirical data. Our approach allows the physician to identify the most promising solutions and thus the best one in terms of reducing work time and risk. The resulting schedule maximises the vaccine delivery rate.