# A Dynamic Framework for Community-Facility Siting with Inter-Community Competition
## 7 Conclusions  
This study proposes a framework for the community-facility location problem, which includes a bi-objective multi-scenario dynamic model as its core, along with a comprehensive set of methods for data acquisition and processing and model computation. The newly proposed model optimizes two objectives: service supply efficiency, reflected by the service supply rate (SSR), and social equity in the service distribution, represented by the service distribution Gini coefficient (SDGC). Additionally, considering the facility number uncertainty and the potential competition among communities for these facilities, the BOMSDM introduces a multi-period incremental strategy and establishes dynamic facility-community allocation strategies that vary according to three scenarios: facility insufficient, facility sufficient, and facility redundant. This framework enables the construction of a dual dynamic model that incorporates both temporal and spatial dimensions. The model is solved using the constrained NSGA-II algorithm, yielding Pareto optimal solutions for SSR and SDGC. To validate the effectiveness and superiority of the BOMSDM, we compared it with three other models: a random allocation non-incremental model, a random allocation incremental model, and an average allocation non-incremental model. We took the allocation of recycling stations across 83 communities in Shaoxing City as a real-world case. The experimental results demonstrate that, compared to real-world solutions, the proposed model significantly improves the efficiency of service provision and social equity in service distribution while also promoting a more balanced distribution of community facilities across communities. Compared to other models, the incremental and dynamic facility-community allocation strategy of the BOMSDM helps reduce the number of new facilities constructed or relocated, enhancing the economic feasibility of facility development while more efficiently achieving the efficiency and equity goals set by the model. Furthermore, empirical validation reveals that when facilities are insufficient, the BOMSDMmay prioritize the community allocation rate, compromising overall efficiency and equity to reduce inter-community competition. However, as facility redundancy increases, the gap between the BOMSDM and random allocation models gradually diminishes. This study addresses the complex issues of facility location and resource allocation, providing theoretical foundations and optimization solutions for decision-makers. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15010402/s1](https://www.mdpi.com/article/10.3390/app15010402/s1)]([https://www.mdpi.com/article/10.3390/app15010402/s1](https://www.mdpi.com/article/10.3390/app15010402/s1)), Table S1: The detailed Pareto solutions produced by BOMSDM in Scenario I with P = 72; Table S2: The detailed results produced by 4 models in three scenarios; Table S3: The detailed results produced by 4 models with different R values. Conceptualization, S.Z. and H.H. ; methodology, S.Z. ; software, S.Z. ; validation, A.D.; formal analysis, A.D.; writing--original draft preparation, S.Z. ; writing--review and editing, H.H. ; visualization, S.Z. ; supervision, H.H. ; funding acquisition, H.H. All authors have read and agreed to the published version of the manuscript. This research is supported by the Center for Balance Architecture of Zhejiang University (Project No: K Heng 20203512-02B, Index and planning methods of resilient cities) and by the Zhejiang Federation of Social Sciences (Project No: 2024-18, Research on the Spatial Mechanism and Institutional Optimization of Rural Civilization Construction in Zhejiang in the New Era). Not applicable. The raw data supporting the conclusions of this article will be made available by the authors upon request. The authors declare no conflicts of interest. The chromosome structure in BOMSDM comprises a set of candidate points with a specific quantity \(p^{t}\).