Healthcare services provided by hospitals generate healthcare wastes which are considered as one of the most complex types of waste generated by institutions. Although a percentage of hospital waste is considered as hazardous waste that may present various risks to humans, animals and the environment if not managed properly. This paper highlights on-site healthcare waste collection, since a proper internal collection is important in order to minimize the risk to the patients, hospital staff, visitors and the surrounding environment. We focus on determining routes for healthcare waste on-site collection from points of generation of the waste to its interim storage area, with the objective of minimizing the total traveling time, considering the disinfection time of the trolleys, and also minimizing the transportation exposure risk. This multi-objective nature of the problem makes it a special case of the vehicle routing problem with time window (VRPTW) but it is complex compared to the general VRPTW since it has several specific characteristics such as managing the trolleys' departure times and the routes ordering, also the transportation is done by a fleet of trolleys performing multiple routes during each shift thus it is related to the multi-trips vehicle routing problem (MTVRP), also each collection request is delimited by a time window and each collection request specifies the type of waste to collect which can be considered as the multi-commodity vehicle routing problem (MCVRP). We present the mathematical model that we have built for the problem, which results after an appropriate transformation of the problem into a node routing one. This specific problem was inspired by a real world application and does not appear in the literature.