中文摘要：

覆盖问题在设施选址中占有重要的地位，有很高的研究价值和应用前景。在传统理论模型的基础上，从用户满意和服务质量水平的视角探讨逐渐覆盖问题。通过对覆盖函数的描述，对现有选址模型进行了改进，使得模型在实践中更具实用性。考虑到满足不同客户的需求标准和服务的公平性，建立了一个基于服务质量水平的随机逐渐覆盖选址模型，并给出了求解该模型的拉格朗日启发式算法。试验数据验证了该模型和算法在设施选址决策中的有效性。

英文摘要：

The covering problems play an important role in facility location with high research value and application prospects. In this paper, we consider the gradual coverage problems in theperspective of customer satisfaction and service quality based on classical covering models. In order to make the model more practical, we improved the classical location model by thedescription of coverage function. Taking into account different service standards and fairness, a new model based on the level of service quality is proposed. We also solve this model withLagrange heuristic algorithm. Computational results illustrated the effectiveness of the model and algorithm in facility location decisions.