Abstract: To guarantee that the emergency calls can be responded to in time, the government is obliged to implement an effective ambulance location plan. In practice, the emergency medical service (EMS) system works in an uncertain environment with stochastic demand, response time, and travel time. The uncertainty of these factors significantly affects ambulance location planning. However, most recent studies in this field fail to consider adequately the effect of the spatial randomness of demand, since it is difficult to describe quantitatively. As a result, most location plans are not efficient.
In this study, Gaussian mixture model clustering is innovatively utilized to describe the spatial uncertain demand quantitatively. The entire planning region can be re-clustered into several Gaussian-distributed demand areas. Based on the depiction of the spatial randomness of demand, an integer programming model for ambulance location planning is constructed. Additionally, in this model, a strict service preference order is specified among the responsible sites for each demand area. The chance-constrained programming method is used to solve the proposed model.
Two years' data from the Shanghai Songjiang District are used to validate the method proposed. The data from 2013 are utilized to fit the spatial distribution of demand. The data from 2014 are used to test and verify the obtained models. Compare with the location plan which ignores the spatial randomness of demand, the performances of the optimal plan obtained by the proposed method are much better. The experimental results indicate that the spatial randomness of demand can significantly affect the effectiveness of the ambulance location plan. Assumptions without considering spatial randomness will result in lots of unexpected delays. Consequently, the plan obtained is unreliable to implement in practice.
The effects of the spatial randomness of EMS demands are considered in our proposed method. Therefore, the service delay caused by spatial distribution randomness can be significantly decreased. For life-improving projects such as the establishment of the emergency medical services network, reducing delay in rendering emergency care is the basic requirement to increase the public's satisfaction with the healthcare system.

Key words: ambulance location planning, spatial randomness, Gaussian mixture model, chance-constrained programming