With the development of society, public resources for healthcare are increasingly inadequate to meet the demands for the services. Therefore, it is extremely important for policymakers to provide citizens with the most effective healthcare services within the limited available resources. In order to achieve positive effect rescue operations in the Emergency Medical Services (EMS) system, the problems including where to locate the ambulance facilities and how many ambulance vehicles should be allocated to the stations have become the focus of attention. In this paper, we study the problem based on the demand for EMS in Songjiang District, Shanghai, China, followed by the joint planning of Emergency Medical Services management, which typically consists of ambulance facility locations planning and patient's assignment to hospitals. We proposed a modified Double Standard Model (DSM) to maximize the demand points covered at least two times within the minimum coverage criteria. The problem is solved by integer linear programming technique with the CPLEX software and we make a comparison between the solutions and the locations which exist in the emergency system used by the Songjiang emergency center. Our results show that the demand coverage rate and response time can be efficiently improved through relocating the current facilities without additional vehicle resources.

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Disasters such as hurricanes, earthquakes and floods continue to have devastating socioeconomic impacts and endanger millions of lives. Shelters are safe zones that protect victims from possible damage, and evacuation routes are the paths from disaster zones toward shelter areas. To enable the timely evacuation of disaster zones, decisions regarding shelter location and routing assignment (i.e., traffic assignment) should be considered simultaneously. In this work, we propose a risk-averse stochastic programming model with a chance constraint that takes into account the uncertainty in the demand of disaster sites while minimizing the total evacuation time. The total evacuation time reflects the efficacy of emergency management from a system optimal (SO) perspective. A conditional value-at-risk (CVaR) is incorporated into the objective function to account for risk measures in the presence of uncertain post-disaster demand. We resolve the non-linear travel time function of traffic flow by employing a second-order cone programming (SOCP) approach and linearizing the non-linear chance constraints into a new mixed-integer linear programming (MILP) reformulation so that the problem can be directly solved by state-of-the-art optimization solvers. We illustrate the application of our model using two case studies. The first case study is used to demonstrate the difference between a risk-neutral model and our proposed model. An extensive computational study provides practical insight into the proposed modeling approach using another case study concerning the Black Saturday bushfire in Australia.

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