摘要
指派矩阵构造是指派问题应用研究的难点,在作战应用领域展开指派矩阵构造专题研究.文中回望了1914年Lanchester关于"兰氏"平方律作战过程取胜条件与剩余兵力的分析结果,以及1996年本文第一作者提出的关于"兰氏"平方律作战过程存在胜负的情况下其作战持续时间计算的数学模型,提出了关于"兰氏"平方律作战过程在作战双方势均力敌的情况下作战持续时间的数学模型.综合运用上述的已有理论与新建理论,建立了取胜矩阵、时耗矩阵、兵力耗损矩阵的一体构造模型.该一体构造模型从作战系统的4类可知数据出发,对于具体的多部队参战的作战过程均能构造出具体的取胜、时耗、兵力耗损数值矩阵.最后给出了取胜、时耗、兵力耗损矩阵的一个一体构造实例,并运用(n×m)-k缺省指派问题理论对该实例求得了其最多K胜条件下的最短时限最少耗费缺省指派最优解.
Assignment matrix constructing is the. hardest problem in the research area of assignment problem application. This paper is a special research for assignment matrix constructing in the area of military affairs. This paper returns to the combat dynamics theories and analytical results concerning wining condition and surviving force presented by Lanchester in 1914. The mathematical model calculating the duration of battle is stated which was presented by the first author of this paper in 1996 for the first time if the battle exists the victory or defeat for Lanchester square law operation process. The mathematical model calculating duration of battle is presented when the initial fighting force of Red Army is equal to the initial fighting force of Blue Army. Applying above mentioned theories synthetically, a model system constructing win matrix and duration matrix and surviving matrix is built. Three numeric matrices, win matrix and duration matrix and surviving force matrix, can be got by the model system for any Lanchester fight course since those needed initial data in the model system can be known. At last a real example constructing such numeric matrices together is given, and the optimal solution which subjected to the shortest time limit and the least cost under the condition of making victory is solved for the example applying absent assignment theory （n×m） --k.
出处
《数学的实践与认识》
CSCD
北大核心
2008年第15期149-156,共8页
Mathematics in Practice and Theory
基金
湖北省教育厅科研重点项目(D20083501)
荆楚理工学院科研项目(ZR200708)
