公路收费站点最优设置的数学模型

针对某些公路收费站点过多过密的问题,建立了在收费站间距满足一定要求的前提下,使收费盈利最大化的数学规划模型.同时,针对站点设置问题的特殊性,将一个复杂的带有条件约束的非线性整数规划问题转化为一个具有简单约束的线性整数规划问题.并针对整数问题求解的复杂性,提出简化的求解方法.最后,以重庆一国道某路段的收费站分布状况为例进行了实例计算分析,结果表明本文所提出的模型是合理和有效的.

A mathematical model for the optimal location of toll stations on the highway

A mathematical programming model is proposed in this paper to solve the problem that the intervals between existing toll stations are too small on some highways. In the model,the profit charged from tolls is maximized under the restrictions that separations between toll stations are limited within a given value.Considering the characteristics of the toll station location problem,this complicated nonlinear integer programming problem with conditional constraints is thus converted to a simple linear integer programming problem.In order to reduce the solution complexity of integer programming,a simplified approach is put forward.Finally,one National Highway in Chongqing is taken as an example to illustrate the application of the model. The results show that the model is reasonable and effective.