Optimization Of The Location Problem On Emergency System

Along with the national modernization advancement, there must be the modernized city emergency system and layout of the fire protection to adapt with them. Location problem is one of the most important long-term policy-making which affects the service way, the quality as well as the service cost and so on, thus it affects the city emergency capability effective display and the resources rational distribution. How to construct the city emergency system and the fire protection layout and enhance the emergency capability has become an important subject in the urban construction and development.This thesis studies the location problem on emergency system using the graphical model the correlation theories and the optimized method. It establishes some location models on the emergency system by combining the actual situation of the emergency system and the characteristics, gives the relevant network optimization method and algorithms under many kinds of conditions.Firstly, it analyzes the location problems algorithm based on the shortest path algorithm, that is, 1-median and 2-median problem. That method is based on the information of the shortest path matrix and vertex weights matrix, and to determined optimal solutions by computing services consumed or price. That algorithm is simple and intuitive. At the same time that is generalized and explained.Secondly, the location problem of single emergency service is analyzed and extended to the multi-facility model. Suppose that the vertexes of the network diagram denote as the emergency services facilities, the constraints mathematical model is established by the emergency conditions and some algorithms of location problems are given.Finally, the network flow problem is studied by considering that the location problem by essentially optimization problems on the network graph. With establishing the network flow matrix and related concept, studying its property, one gets the new idea to solve the network maximum flow based on the flow matrix and gives out the strict mathematics provement from the theories. The thesis adopts the methods of the node flow balance, problem conversion and reducing the matrix order. The application of these methods has important theories meaning and the purpose of the simplified problem.