水利工程中的引水管道的铺设,运输路线的选择和输水路程的确定等问题,都需要寻求其最优解。这些问题都属于多阶段的最优化决策问题。通常解决的方法是:根据贝尔曼(Bellman)最优化原理,把问题分成若干阶段,建立一个递推方程,由最后一个阶段开始,逐次逆推分段寻优作出各阶段的最优化决策,最终使整个过程取得最优化的结果。本文则是将矩阵的概念加以推广和扩充,建立一套适用于多阶段决策问题的运算规则,直接利用摹矩阵的 The laying of diversion pipelines in water conservancy projects, the choice of transport routes and the determination of water transport distance all need to seek its optimal solution. These problems are all multi-stage optimization decision-making problems. The common solution is to divide the problem into several stages according to Bellman’s principle of optimization and establish a recursive equation. From the last stage, The whole process to obtain the best results. In this paper, the concept of matrices is extended and expanded to establish a set of arithmetic rules applicable to multi-stage decision-making, and the direct use of the matrix of matrices