With ageing societies and increasing number of patients, there is a growing need for quality services that help transporting non-urgent patients to hospitals. In logistics, patient transportation problems are usually modeled as a dial-a-ride problem. In a Dial-a-Ride problem, a fleet of vehicles is providing the delivery services between the loading points and the delivery destinations. The demands are known in advance. In most cases the total travel distance of the vehicles is to be minimized. In this paper, we consider a specific dial-a-ride problem, where a single vehicle is used to transport patients to the same hospital. In determining the optimal route, the multiple and different travel needs of patients, such as their maximum travel time, are also taken into consideration. We introduce 4 different mixed integer linear programming models of the routing problem. Finally, the efficiency of the four models was compared using some real-life problems by solving them with a commercial solver.

With aging populations and rising healthcare demands, efficient patient transportation has become a critical challenge, particularly in the context of infection control. In this paper an extended mixed-integer linear programming (MILP) model for optimizing patient transport in urban environments is presented, with a focus on the separate transportation of infectious and non-infectious individuals. The model incorporates time windows, maximum allowable ride durations, and mandatory vehicle disinfection requirements. Experimental results obtained using CPLEX demonstrate that incorporating infection control measures significantly influences both route planning and computational complexity. The proposed approach provides a scalable foundation for future multi-vehicle extensions and cost-based optimization strategies.