中文摘要：

关键路线法（critical path method，CPM）网络计划是项目管理最得力的工具之一．通过研究CPM网络图自身的规律性，给出了从源点到任意节点，以及从任意节点到汇点最长路线的路长计算公式，进而推导出反映总时差与路长关系的定理——总时差定理，并在其基础上，设计出构造等效子网络的简单方法，分析了方法的正确性，且得出该方法的计算复杂度为O（n）．实证表明，该方法简单易行，便于应用．对于时间一费用优化问题，可以用少数几条路线组成的子网络代替由几十条、几百条路线组成的原始网络，使计算工作量得到简化．

英文摘要：

Critical path method （CPM） network is one of the most useful instruments for project management. The relation ship between the activity float and the path length, which shows the fundamental laws of an activity-on-arc CPM networks, is studied in this paper. Two equations about the length of the longest path from start node to arbitrary node and from arbitrary node to end node are given. Relative theories such as ＂Total Float Theory＂ are presented and demonstrated on the basis of the research above. Then, an easy method whose com- plexity is 0 （n） is designed to create the ＂the equivalent sub-network＂ which can be used to simplify the ＂time-cost tradeoff＂ problem. Furthermore, a strict theoretic proof about the new algorithm of the equivalent sub-network is provided. At last, it is proved to be feasible and easy to use through an example. Based on this method, the original network with scores of, or even hundreds of paths can be represented by an equivalent sub-network of less paths which can simplify the calculation.