In developing countries, the demand for old aged people requiring private health care at home is dramatically growing with the improvement of living standards. Since vehicles are used for transferring the medical staff (or doctors) to patient homes, it may be interesting to select a vehicle type based on the cost, capacity, and environmental sustainability (fuel consumption and CO2 gas emission per unit of distance) to maximize profits and social responsibility. In this paper, the first contribution, a new green home health care network for location, allocation, scheduling, and routing problems is developed with uncertain conditions. Another novelty, the time window to serve patients is also considered. In this regard, a novel grey flexible linear programming model is developed to cope with the uncertain nature of costs and capacity parameters that is as one important novelty. Due to this model’s high complexity and difficulty in large-scale instances, this research develops two novel hybrid algorithms. The first hybrid strategy called the HSEOSA algorithm combines the Social Engineering Optimizer algorithm with the Simulated Annealing method. In terms of contribution to the related solution methodology, additionally, the Keshtel Algorithm is incorporated with the Genetic Algorithm called the HGAKA algorithm as the second new hybrid metaheuristic. An extensive comparison among the proposed algorithms is performed to find the most efficient one for the application of home healthcare in real practice. To validate the proposed model, a novel real case study is illustrated in the home healthcare services in Tehran/Iran.
