The vehicle scheduling problem has been extensively studied in the past decades. Yet, most models and methods given in the literature consider only a theoretical scenario where vehicles just have to service the timetabled trips of the input. However, schedules created this way cannot be used in real life, as they should also consider constraints such as refueling, parking, and maintenance, which are all connected to the vehicle servicing the trips. In this paper, we give a set partitioning model for the multi-depot integrated vehicle scheduling and vehicle assignment problem. This model can also be used as a general framework, which can integrate multiple activities based on the rules or regulation of the different possible input scenarios. We give a column generation-based solution method, and demonstrate its efficiency on randomly generated test instances, which treat the refueling of vehicles with two different fuel types as the vehicle-specific activity.