Two Variants of Bi-objective Vehicle Routing Problem in Home (Health)-Care Fields

Abstract

In this research paper, we consider two bi-objectives models, the Vehicle Routing Problem Preferences with Time windows, temporal dependencies, multiple structures and multiple specialties “VRPPTW-TD-2MS” and the Vehicle Routing Problem Balance with Time windows, temporal dependencies, multiple structures and multiple specialties “VRPBTW-TD-2MS”, in Home (Health)-Care “HHC” service field. In this context, The HHC services is mostly assigned to certain persons such as people who have a chronic disease or who have difficulty leaving their houses by offering them medical, social, and/or medico-social services like nursing, dressing, bathing, toileting, feeding, shopping, hygiene assistance, etc. These several services are provided by different public and private home care structures. These structures work together in coordination to provide high HHC quality for patients. Therefore, patients are not in a single structure anymore, but rather at home and need to be served by caregivers. As a result, the problem is no longer limited to the care organization, but also to the construction of optimal tours for the caregivers, the delivery of medicines, and the equipment needed for care. According to our knowledge, our work is different from those made in the literature. Our problem consists to determine the caregivers’ tours while optimizing bi-objective function, which aims to minimize the total traveling time and the total negative preference or the maximal difference workload of caregivers under set of constraints such as time window, synchronization, precedence and disjunction constraints with multiple structures and multiple caregivers’ skills. A benchmark of instances is considered from literature. Cplex (Optimization Software package) is used to solve our problems to obtain efficient solutions.