Emergency facility location and layout are critical to the efficiency of emergency rescue and resource allocation. However, practical emergency scenarios are plagued by two key challenges: the risk of facility failure due to various uncertain factors and the presence of complex polygonal barriers (including convex and concave polygons) that hinder transportation. Existing studies often overlook concave polygonal barriers or fail to prioritize time satisfaction, a core demand in emergency response. To address these gaps, this paper proposes a reliable emergency facility location optimization model with the objective of maximizing time satisfaction, considering constraints such as capacity, cost, and demand. The model integrates three key methods: a convex hull algorithm to convert concave barriers into convex ones for simplified calculation, a path optimization algorithm to find the shortest bypass routes around barriers, and an Artificial Ecosystem Optimization (AEO) algorithm to solve the nonlinear programming model. Through numerical experiments (single-facility, multi-facility, and medium-scale scenarios) and a practical case study in the Meknès region of Morocco for ambulance deployment, the feasibility and effectiveness of the model and algorithms are verified. The results show that the model achieves high time satisfaction (all above 0.8, with most exceeding 0.9) and efficiently optimizes facility locations and resource allocation. Sensitivity analysis indicates that increased failure risk parameters ($\alpha$ and $\theta$) lead to a gradual decrease in average time satisfaction. This research provides a systematic mathematical model and practical method for emergency facility location decision-making, effectively addressing the challenges of complex barriers and facility failure.

The issue of emergency facility location is a long-term strategic issue, and the complexity and diversity of the decision-making environment force decision-makers to focus on multiple objectives when making location decisions. We develop a multi-objective optimization system centered on cost-effectiveness, service balance, and fairness, targeting three core objectives: minimizing total costs, minimizing differences in service quality among demand points, and minimizing material shortage gaps between demand points. To address the issue of limited facility service capacity induced by material shortages, we establish a multi-objective optimization model for the reliable location of emergency facilities. By combining the model’s characteristics with the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and an elite retention strategy, the Pareto frontier solution set of the multi-objective model is obtained, and the model’s feasibility is verified through various examples of different scales. Finally, sensitivity analysis was conducted on the reliability location model of emergency facilities under different disruption risks using the control variable method, and the topology structure of the reliability location allocation network for emergency facilities under different disruption situations is obtained. The research findings provide decision-makers with actionable references and technical support for selecting reliable locations for emergency facilities amid disruption risks.