GRASP Combined with ILS for the Vehicle Routing Problem with Time Windows, Precedence, Synchronization and Lunch Break Constraints

Abstract

In this era of pandemic especially with COVID-19, many hospitals and care structures are at full capacity regarding availability of beds. This problem leads to ensure giving specific cares to people in need either in illness or disability in their own homes. Home Health Care (HHC) proposes this kind of services for patients demanding it. These services have to be done at the request of the patient which appears to be the client in a way that gives satisfaction to the requester of the service. Often, these demands are bound by a specific time that the workforce (caregivers) are obligated to respect in addition to the precedence (priority) constraint. The main purpose of the HHC structures is to provide a service that is good in term of quality, minimize the overall costs and shorten the losses. To reduce the costs of these HHC structures, it is mandatory to find comprehensible and logical ways to do it, for it is not permissible to touch the caregiver salary, HHC structures find themselves in the obligation to optimize by other means such as reducing the travel cost. Note that these structures give cares in one's home, which means that the travel aspect is important and is considered the core spending charges of the institution. Another fact is the satisfaction of the patients toward caregivers; this is an essential element to optimize in order to obtain a good quality service, to give a realistic aspect for the problem the lunch break of caregivers is introduced as a parameter. For those arguments, a conception of an efficient planning of caregivers involves using decision tools and optimization methods. A caregiver (vehicle) is attributed to a patient (customer) to do a number of cares with several options in accordance to the customer wishes like time windows requirement often specified by the client, the priority or precedence constraints are usually performed if a care have to be performed before another and could need the intervention of more than one caregiver and must have at least one lunch break a day and it is not always taken at a set time of the day and must be versatile to optimize customer demand satisfaction. To resolve this issue which is called VRPTW-SPLB, a mathematical model of the problem is proposed and explained as a Mixed Integer Linear Programming (MILP) and a greedy heuristic based on a Greedy Randomized Adaptive Procedure (GRASP) is proposed, two strategies based on local search and two metaheuristics, and a metaheuristic resultant of an hybridization of the two metaheuristics. At the end of the paper, results are shown on a benchmark extracted from the literature.