Abstract: Node slack is of great importance in CPM network, and it is the most intuitive and the simplest for computing and applications in a variety of slacks. This paper presents three new properties of the node slack, and the slack theorem and characteristic path theorem are deduced. After that, an introduction of applications of node slack in finding the second critical path and constructing equivalent sub-network to simplify large-scale network in time/cost trade off problems is made, and the methods are theoretically proved.

Key words: CPM network, node slack, characteristic path theorem, network simplification