To meet the needs of rapid emergency treatment of public health emergencies, as a key measure to effectively control the spread of the epidemic, planning the location and scale of emergency medical facilities in advance is of great significance, and it saves construction costs and social resources. Focusing on sudden epidemic situation with uncertain demand, this work studies the optimization decision of location selection and construction scale of emergency medical facilities. We establish a bi-objective integer programming model with the objectives of minimizing both total construction costs and the difference between the ratios of demand to supply of bed resources. According to the characteristics of the model, the exact epsilon-constraint algorithm and a heuristic algorithm based on the principle of proximity are designed to solve the problem, and the classical non-dominated sorting genetic algorithm(NSGA-II) is used in comparative analysis. Numerical results verify the effectiveness of the proposed algorithms. The obtained conclusions can serve as valuable application guidance for the construction site selection and scale decision of the emergency medical facilities, and provide theoretical supports for managers to make operational decisions.