A Metaheuristic Approach Based on a Mathematical Model for Home Care Worker Scheduling and Routing Issues
Abstract
The medical system is transitioning from hospitalisation to home care, and the World Health Assembly has indicated that the proportion of care-dependent older individuals in Europe will significantly rise in the next generations. Therefore, a scientific strategy for this region is crucial in enhancing the community's health. This study seeks to formulate a mathematical model for the Residential Healthcare Planning and Scheduler Issue and to resolve it using the Simulated Annealing (SA) technique, while accounting for real-world factors such as staff transportation and client circumstances. The research enables dependent treatments for clients, allowing them to request various amenities in any combination and designated time window for each service. The mathematical description of the issue in question is encoded in the programs of a renowned commercial optimisation tool. The SA method addresses extensive problems that the system cannot resolve. Sensitivity evaluation is undertaken for the critical factors, specifically the number of amenities and the number of patients utilising various interdependent amenities. The findings indicate that when every client can request an unlimited number of amenities with any interrelation, the complexity of the issue escalates; yet, the SA method can effectively address large-scale cases, yielding satisfactory solutions with reduced computational energy. The SA algorithm demonstrates commendable efficacy for substantial situations. The primary elements influencing the final value and duration of the issues are the number of clients and the number of customers requiring interconnected different services.