All over the world both the health and logistics sectors experience strong growth. Taking into account demographical change, especially the relative increase of the elderly as part of the whole population, the healthcare market as well as the share of logistical applications in health care is expected to rise even further. In this work, we focus on a patient transportation problem for the Arbeiter Samariter Bund (ASB), an emergency medical service in Vienna. The organization has to perform a large number of patient transports every day and, in addition, has to respond to arising emergency calls. Assigning vehicles of a fleet to given transportation requests is usually modeled as a static dial-a-ride problem (DARP), which is well studied in the literature [1], [2]. However, there are significant differences between the formulations of the DARP in the literature and the real world problem tackled here, which makes the problem interesting and challenging to solve. In the considered application, a certain number (about 60%) of transportation requests is known in advance, whereas other requests are occurring throughout operations. The ASB aims at planning the allocation of the vehicles to requests for the next day in a way that daily operations run as efficiently as possible. On the day itself, suggestions for allocating requests to vehicles will be given to the dispatchers. Therefore, a stochastic and dynamic variant of the DARP is considered. Based on historical data from ASB, stochastic demand and travel-time models will be used. This extends the model proposed in [3], where only stochastic information about expected return trips of patients is considered. An additional challenge is the sheer size of the problem that has to be solved. The number of requests scheduled at the ASB every day as well as the number of vehicles in the fleet are large compared to the classic DARP instances used in the literature [1]. The problem instances consist of a fleet of around 120 vehicles and the ASB serves approximately 800 - 1000 patient transportation requests a day. The problem is solved in a two-phase approach, in the first phase known as well as sampled transport requests will be combined in order to build a starting solution for the day of operations. In the second phase, new requests are quickly inserted in the solution replacing the sampled requests, thereby allowing fast response times if reasonable. The solution is then further optimized in a background process. This paper will present two main aspects of the proposed approach: the stochastic models and a restricted dynamic programming approach for solving the initial problem.