广义最大覆盖模型在消防站优化选址中的应用

Application of the general maximum covering model to the locality choice of fire stations

针对目前我国城市消防站建设存在的数量不足、责任区面积过大、选址缺乏科学性等问题,引入广义最大覆盖模型,探讨城市消防站的优化选址方法。广义最大覆盖模型很好地解决了传统最大覆盖模型中假设覆盖度为二元值的缺陷,通过分段递减函数,将覆盖度表示为0～1之间的连续值,实现了供应点对所有需求点的覆盖。同时,本研究还考虑不同区域的火灾风险等级并设定了相应响应时间限值,通过对最短响应时间和响应时间限值的比较,得出候选消防站点对各个需求点的覆盖度水平。通过实例对广义最大覆盖模型的有效性进行验证,并利用LINGO软件进行求解。研究表明,广义最大覆盖模型可实现供应点以不同程度覆盖所有需求点,更适用于消防站类应急设施的选址问题。

The present paper is inclined to introduce our research results on fire stations location-allocation method. As a matter of fact, the location-allocation of fire stations in China is lack of science methods, and the fire stations in most parts of the country are chosen with no proper reasons at all. Aiming to solve the current problem, this paper has been tying to apply the general maximal covering model in the locality choice of fire stations. Generally speaking, the socalled traditional maximal covering model is supposed to be binary. The coverage can only be 0 or 1, in which 1 means the node can be covered while 0 means the node cannot be covered. In so doing, some demand nodes might not be served. In fact, the purposes of the emergency facilities location-allocation are to ensure all of the demand nodes can be covered by the facilities. Therefore, the general maximal covering model can be expected to overcome the above shortcomings. That is to say, unlike the traditional maximal covering model, the improved one can make all of the nodes well served in different coverage levels. In addition, this paper has also taken into account of the fire risk categories in different areas and the time limits of different risk categories. We decided the coverage levels by comparing the traveling time with the time limits. Furthermore, an example was also given to test the rationality and applicability of the improved model with the problem solved in virtue of LINGO. The solution has also been done by using the traditional covering model. Thus, the comparison of the two results helps to show the strong points of the improved model stated in this paper, indicating that the improved model helps to cover all of the demand nodes in varying degrees and solve the locality choice problem of emergency facilities such as fire stations more satisfactorily.