Periodic Vehicle Routing Problem with time windows for Home Dialysis Care

In this paper we address a particular issue dealing with the problem of building periodic tours for the delivery of consumables required for home dialysis, taking into account the patient's storage capacity and the time windows for patient visits. The aim is to visit patients according to their preferences while respecting storage capacity and minimizing the costs incurred by the association responsible for delivery. To solve the problem, we proposed exact solution methods. For the optimal solution we have given two distinct mathematical formulations, the first considers hard time window constraints and the second considers them as flexible by adding a delay penalty in the objective function. A comparison of the two models on an instance of 9 patients enabled us to verify that the two models would lead to the same solution in the case of wide time windows. A second comparison was carried out on the same instance with tighter time windows, showing that the model with hard constraints failed to find a solution, unlike the model with soft ones, which provided a solution with a delay penalty.