A decomposition approach for the prioritised home health care problem with synchronised visits and multi-period planning

Abstract

This study focuses on a home health care routing and scheduling problem (HHCRSP) with time based priorities and the option of not visiting all patients. This problem arises in situations when the HHC provider has insufficient number of caregivers available and/or faces higher than usual demand over a period of time. Determining the routes and schedules of available limited caregivers to match prioritised patients is, therefore, a highly critical task for many HHC providers. The patients that potentially cannot be serviced at their homes, can be offered a phone-call service or a time slot out of their requested time windows. A distinctive feature of the problem we are dealing is that a patient may need various services from a team of caregivers at the same time. Hence, this problem is a prioritised home health care routing and scheduling problem (PHHCRSP) with a multi-period planning horizon and synchronised visits. We extend the single caregiver model proposed by Cinar et al. (2021) to allow for multiple caregivers with various capabilities and synchronised visits. We then propose a new spatial–temporal decomposition with patient filtering (STDPF) approach to solve this problem in operational time. This method combines multi-dimensional temporal and spatial decomposition approaches together with a prioritisation scheme considering the care requirements and priorities. Computational tests on realistically large benchmark instances show that the proposed method provides high quality solutions within reasonable computational times. The flexible and scalable decomposition strategies used in the STDPF, together with the use of solvers, allow our approach to handle any additional constraints and even larger problem instances.