###### Abstract  
Equal accessibility to healthcare services is essential to the achievement of health equality. Recent studies have made important progresses in leveraging GIS-based location-allocation models to optimize the equality of healthcare accessibility, but have overlooked the hierarchical nature of facilities. This study developed a hierarchical maximal accessibility equality model for optimizing hierarchical healthcare facilities. The model aims to maximize the equality of healthcare facilities, which is quantified as the variance of the accessibility to facilities at each level. It also accounts for different catchment area sizes \(\theta\), and distance friction effects for hierarchical facilities. To make the optimization more realistic, it can also simultaneously consider both existing and new facilities that can be located anywhere. The model was operationalized in a case study of Shenzhen, China. Empirical results indicate that the optimal healthcare facility allocation based on the model provided more equal accessibility than the status quo. Compared to the current distribution, the accessibility equality of tertiary and secondary healthcare facilities in optimal solutions can be improved by 40% and 38%, respectively. Both newly added facilities and adjustments of existing facilities are needed to achieve equal healthcare accessibility. Furthermore, the optimization results are quite different for facilities at different levels, which highlights the feasibility and value of the proposed hierarchical maximal accessibility equality model. This study provides transferable methods for the equality-oriented optimization and planning of hierarchical facilities. e 27 September 2021 27 October 2021 27 October 2021 27 September 2021 27 October 2 impacts have significantly highlighted health and safety issues and the rational planning of healthcare resources [12; 13]. However, the distribution of healthcare services decided in the traditional manner often do not provide equal accessibility to all [3; 14; 15; 16]. There are significant disparities in healthcare accessibility across different locations or different socio-economic groups (e.g., natives vs. immigrants, high-income vs. local income, and the elderly vs. the young) [17; 18; 19], which has important spatial/social equity implications [20]. In Shenzhen, China, the study area, significant inequality in healthcare accessibility has also been revealed by existing studies [16; 21]. The irrational distribution of healthcare facilities and inequality of accessibility make a strong call for the optimization of healthcare facilities. Academia from fields such as public health and geography have paid increased attention to the optimization of healthcare facilities. A series of optimization models have been developed, which are usually known as the location-allocation models [22; 23]. Typically, these models set up one or more objective functions and a set of constraints [24]. Efficiency and equality are the most important objectives for allocating public facilities to different sites [25]. However, most of existing studies focus on the efficiency objectives such as minimizing the numbers or cost of facilities, maximizing the coverage of facilities, and minimizing the travel cost between consumers and facilities [26; 27]. By contrast, little attention has been paid to equality of facilities distribution in location-allocation studies, partially due to the difficulty in modelling and optimizing equality [4]. Recently, an innovative stream of studies has considered spatial/accessibility equality in the location-allocation analysis [28; 29; 30; 31]. The maximal accessibility equality (MAE) model developed by [PERSON] and [PERSON] [28] is a novel and helpful method for researchers and practitioners who are interested in improving the equality in demanders' accessibility to public services (e.g., healthcare services). However, the development and implementation of the MAE model are still confined to single-level facilities.