The multi-period home healthcare routing and scheduling problem with electric vehicles

This paper studies the multi-period home healthcare routing and scheduling problem with homogeneous electric vehicles and time windows. The problem aims to construct the weekly routes of healthcare nurses, which provide service to the patients located at a scattered geographic area. Some patients may require to be visited more than once in the same workday and/or in the same workweek. We consider three charging technologies; normal, fast, and super-fast. The vehicles might be charged during the working day at a charging station or at the end of the working day at the depot. Charging a vehicle at a depot at the end of a working day requires the transfer of the corresponding nurse from the depot to her/his home. The objective is to minimize the total cost that comprises the fixed cost of utilizing healthcare nurses, the energy charging costs, the costs associated with depot-to-nurse home transfer services, and the costs of a patient left unserved. We formulate a mathematical model and develop an adaptive large neighborhood search metaheuristic that has been efficiently crafted to handle specific problem features. We conduct extensive computational experiments on benchmark instances to assess the competitiveness of the heuristic and to deeply analyze the problem. Our analysis shows the importance of competency level matching as mismatching competency levels could increase the costs of home healthcare providers.