Abstract Generally, in Home Health Care (HHC) logistics, caregivers which are started from a pharmacy are scheduled and routed to do different care services at patients' home. At the end, they go to their laboratory to update the patients' health records. In addition to scheduling and routing of the caregivers, there are some other optimization decisions which can increase the competitive advantages of HHC organizations as a supply chain network. The location decisions of the pharmacies and laboratories and the assignment of patients to the nearest pharmacies are two of the several important logistics factors for an HHC organization. The literature shows that the green emissions and sustainability achievements for HHC logistics are still scarce. To cover more logistics and sustainability factors and make the HHC more practical, this study contributes a Green Home Health Care Supply Chain (GHHCSC) for the first time by a bi-objective location-allocation-routing model. Already applied successfully to this research area, the Simulated Annealing (SA) is also employed in this study. Another main innovation of this paper is to propose a set of new modified SA algorithms to better solve the proposed NP-hard problem. As a bi-objective optimization model, the epsilon constraint method is also utilized to check the algorithms’ results in small sizes. By using some multi-objective assessment metrics, the algorithms are compared with each other and their performance is evaluated. As such, some sensitivity analyses are performed to reveal the efficiency of the developed model. Finally, some managerial insights are deployed to achieve the sustainability for the HHC organizations.