中文摘要：

针对项目进度计划管理中如何寻找CPM网络图中任意阶次关键路线等问题，在分析了自由时差概念和特性的基础上提出了七级标准工序、k级特征值和k级标准路线等新概念，推导出自由时差定理和特征值定理，进而利用这些概念和定理给出k阶次关键路线的求法——最小特征值法，分析了算法的正确性，并且得出该算法的计算复杂度为O（n^2）．证明了该算法可以通过局部寻优实现全局寻优．最后结合应用举例论述了该方法的应用范围及特点．

英文摘要：

To Solve problems such as how to seek any k-th order path in CPM network in project scheduling, some new conceptions： The k-th order normal activity, the k-th order eigenvalue and the k-th order normal path, are given. The free float theorem and eigenvalue theorem are deduced by analyzing these conceptions and the characteristics of free float. Then, an algorithm of seeking the k-th order critical path--the smallest eigenvalue algorithm whose complexity is O （n^2） , is proposed according to these conceptions and theorems, and correctness of the algorithm is analyzed. It is proved that the algorithm could achieve whole optimum by partial optimization. Finally, some properties and scope of this method are given by an example.