A variable neighborhood search for home care scheduling under chargeable overtime and preference matching

This paper addresses a home care (HC) scheduling problem faced by a real provider working in New York City area, USA. HC scheduling is an extension of vehicle routing problem with specific constraints and characteristics. The addressed problem is also a matching problem since it considers the caregiver-client matching which depends on the value of each pair's satisfaction. The novelties of our problem lie in chargeable overtimes, preference matching and several specific constraints from the provider. A mathematical model for the problem is provided with the objective of minimizing the unmatched preferences, the overtime cost paid by provider and the total caregivers' travel time. A variable neighborhood search algorithm is also proposed to solve the problem and tested on a real instance from considered HC provider. Numerical results show that the proposed algorithm can efficiently provide high quality solutions on real-sized instances.