New decomposition methods for home care scheduling with predefined visits

Abstract

The continuous aging of the population and the desire of the elderly to stay in their own homes as long as possible has led to a considerable increase in the demand for home visits. In this context, home care agencies try to serve more patients while maintaining a high level of service. They must regularly decide which patients they can accept and how the patients will be scheduled (care provider, visit days, visit times). In this paper we aim to maximize the number of new patients accepted while ensuring a single provider-to-patient assignment and a consistency of the visits times for every patient through the week. To solve this problem, we propose an extension to an existing logic-based Benders decomposition. Moreover, we present a new pattern-based logic-based Benders decomposition and a matheuristic using a large neighborhood search. The experiments demonstrate the efficiency of the proposed approaches and show that the matheuristic can solve all the benchmark instances in less than 20 s.