Assistenza sanitaria a domicilio: problemi multi-obiettivo d’instradamento di veicoli con bilanciamento di carico e fidelizzazione paziente-infermiera

In this Thesis we tackled a real life problem concerning the management of a Home Health Care service, where nurses provide medical treatments directly at patients home. The weekly master problem consist of assigning to each service request a day of week and a nurse according to the service frequency while ensuring a minimum elapsed time between successive treatment deliveries, and to optimally sequence the requests assigned to each nurse on each day of the week. The objective function is a weighted sum of the priorities of each stakeholder: the service provider aims at minimizing the time nurses spend travelling from a patient to the next as well as overtime work; nurses aim at workload balancing; patients would like to be treated by the same nurse over time. We proposed a MILP formulation for this problem, investigated two mathe- matical programming based approaches, namely Column Generation and Ben- ders Decomposition, and we developed a procedure computing a valid lower bound. Real cases could not be solved by such approaches so metaheuristics have been investigated as well. Adaptive Large Neighborhood Search and Variable Neighborhood Search based methods have been developed and applied to this problem, devising ad hoc moves and efficient feasibility check procedures that exploit the problem structure. A large experimental campaign has been carried out, including an analysis of real data characteristics, which highlights pros and cons of each method and confirms the viability of the approach to solve realistic instances.