空中加油问题模型建立及其解法

The Models of in-flight Fueling of the Fighter Problem and Their Solutions

空中加油问题是一个关于在飞机飞行过程中,辅机在空中给主机加油来提高主机直航能力的问题.该题的要求是在辅机架数n一定的情况下,确定最优作战方案及主机的最大作战半径.对于问题1和问题2,首先给出了一般情况下的飞机调度的数学模型,然后用穷举法求出了n≤4情况下的最优作战方案及主机的最大作战半径rn,然后用归纳法推导出了n为一般情况下rn的上下界,最后给出了判断最优作战方案的必要条件.问题3中,给出了与问题1、问题2类似问题的求解结果.问题4中,首先求出了n≤4时空军基地的选址和最优作战方案,然后给出了n为一般情况下,最优作战方案和基地选址的通用数学模型.问题5中,在主机最快到达目的地并返回的条件下,给出了主机的飞行路线和最优作战方案;在满足辅机架数最少的条件下,给出了作战方案,并用MATLAB求出了满足该条件时的最少辅机架数的上界为248架.另外,给出了一些新的定义方法和定理并全部给予证明.

In - flight fueling of the fighter problem is about the accessorial plane adds gasoline to the main plane during flighting process, in order to increase direct - fly capability. This problem＇s requirement is under the condition that the number of the accessorial plane set is fixed, then to optimizate the battle scheme and the largest radius of the main plane. As for question No. 1 and No.2, This article give out a mathematic model first to arrange planes in the normal situation, second, illustrates the optimaization battle schema and the largest radius of the main plane using（qiong ju fa） ,third,use induction method to settle upper and lower limit, at last, give out the necessary condition to verdict the scheme. For the question No. 3 which is give out the results of the matter which is similar to question No. I and No.2. For question No.4, first, seek out the optimizate scheme of the air force and base＇s location,then,present the mathematical model for the optimum scheme of the air force and base＇s location in normal situation. For question No. 5, under the condition that the main plane must arrive and return at the fastest speed, give out the main plane＇s flight route and the battie scheme; under the condition that the accessorial plane sets is the least, point out the battle scheme, then using MATLAB to reach the result that 248 sets is the upper limit. In addition, the article has given out some new definitions and theorems and all have been proved!