Mathematical Model for Dial a Ride Problem with Time Windows, Case: Hemodialysis Patients Transportation

End stage renal disease (ESRD) has become a very common disease nowadays as the number of patients is increasing. As a result, an increase in the number of dialysis treatment is noticed. Many dialysis patients treated at dialysis facilities require six trips each week, three trips to dialysis centers and three trips from the dialysis centers. This comes to more than 300 trips each year per patient. This paper focuses on the transportation of patients undergoing the hemodialysis, as they request rides to their treatments. The transportation problem for hemodialysis patients comes with challenges such as the scheduling problems, extra care and support for the patients and the increased cost of the trips. This paper focuses only on reducingthe total cost of transportation. We consider the hemodialysis patients' transportation problem as the problem of determining an optimal routing for a fleet of vehicles used to cover the regular trips requested. The rides must respect some real-life constraints such as the maximum vehicle capacity, availabilityof the vehicle, patient's schedule … etc. The study focuses on the dial a ride problem with a time window (DARPTW), which is a type of Vehicle Routing Problem (VRP) that is known in the literature as a complex combinatorial optimization problem related to transportation. Mainly used for transporting individuals with requests. In which a set of users must be picked up from an originlocation and they must be delivered to a destination location. The problem is modeled mathematically as a static dial a ride problem (DARP) where the aim or the objectif function is to minimize the total cost of the transportation.