Given a fleet of identical vehicles and a set of n clients to be served from a single depot, the well-known vehicle routing problem (VRP) consists in serving each client (with a deterministic demand) once with a unique vehicle, with the aim of minimizing the total traveled distance. In this work, the basic VRP is extended within a medical environment, leading to MVRP (for medical VRP). Indeed, the depot is typically a laboratory for blood analysis, and a client is assumed to be a medical location at which blood samples should be picked up by a vehicle. In order to have efficient tests at the laboratory, at most 90 minutes should elapse between the release time of the blood sample and the delivery time at the laboratory. In addition, only a proportion of the demand is known in advance and the travel times depend on the traffic conditions. A fleet of non-identical vehicle is considered (with different speeds and capacities), and each location has to be visited anytime a blood sample is available. Finally, medical items should be daily delivered from the laboratory to some medical locations. A transportation cost function with three components has to be minimized. Solution methods are proposed, which are able to account for all the specific features of the problem. The experiments highlight the benefit of considering diversion opportunities (which consists in diverting a vehicle away from its planned destinations).