We develop neutrosophic goal programming models for sustainable resource planning in a healthcare organization. The neutrosophic approach can help examine the imprecise aspiration levels of resources. For deneutrosophication, the neutrosophic value is transformed into three intervals based on the truth, falsity, and indeterminacy-membership functions. Then, a crisp value is derived. Moreover, multi-choice goal programming is also used to get a crisp value. The proposed models seek to draw a strategic plan and long-term vision for a healthcare organization. Accordingly, the specific aims of the proposed flexible models are meant to evaluate hospital service performance and to establish an optimal plan to meet the growing patient needs. As a result, sustainability’s economic and social goals will be achieved so that the total cost would be optimized, patients’ waiting time would be reduced, high-quality services would be offered, and appropriate medical drugs would be provided. The simplicity and feasibility of the proposed models are validated using real data collected from the Al-Amal Center for Oncology, Aden, Yemen. The results obtained indicate the robustness of the proposed models, which would be valuable for planners who could guide healthcare staff in providing the necessary resources for optimal annual planning.