中文摘要：

随着中国人口老龄化程度的加深与生活水平的提高，社会对家庭护理的需求大大增加。针对多服务多护理中心选址问题，建立了一个混合整数数学规划模型，以同时求解多个时间段的选址决策和服务能力决策。其中重点研究了响应时间上限约束对决策的影响，弥补了现有家庭护理中心选址没有考虑到响应时间约束与顾客满意度的不足。数值试验结果与敏感度分析验证了模型的有效性。

英文摘要：

With the rapid aging of the Chinese population and the improvement of living condition, the need for home care services is increasing. For the multi-service multi-facility location problem in home care, this paper proposes a mixed integer mathematical programming model to determine location and service capacity simultaneously. The service response time is considered in the model by setting an upper limit. Numerical experiments and sensitivity analysis are performed to validate the performance of the proposed model.