Health services research aims to improve population health by studying the organization, delivery, and financing of healthcare services. While the field has made progress in defining its boundaries and core research topics, our literature survey revealed a lack of attention given to the management, cost, and policy aspects of healthcare systems (SCs). Moreover, the readiness of the system to handle supply policy and device deficiencies, especially during the pandemic, was rarely mentioned. Unplanned urban growth, characterized by reduced open spaces, deteriorating infrastructure, and changes in biological morphology, has led to an uneven distribution of urban amenities, facilities, and healthcare services. This research proposes two reliable models for site selection in a major hospital in Hong Kong, considering uncertainty levels, infeasibility tolerance, and reliability. We examine two categories of uncertainty—symmetric and bounded—and provide a solution with a nominal objective function value of 121.37. By considering 23 uncertain parameters with specific tolerance levels, we extend the processing time of uncertain tasks to ensure feasibility. However, the objective function value decreases due to violations of intermediate due-dates and decreased overall production. A comparative analysis is presented to evaluate the solution and address scheduling challenges under uncertainty using a specified probability distribution function. The study concludes by introducing justice and health problems, outlining four typical strategies, and emphasizing the importance of the effective management of systems, components, and procedures for the production, distribution, and administration of medications and healthcare supplies. This research contributes to fairness in health systems and population health at local, national, and global levels, addressing health inequity and promoting public dialogues on the subject.