Abstract: A paradox in spliced network is found in this paper, that is when adding a time constraint but in two different types between activities may produce different longest path. A whole new presentation of spliced network is given by studying the paradox. The new spliced network presentation is quite simple but also unified with the classic CPM network in forms. This unification not only helps to solve the problems of how to calculate the time parameters, activity floats and how to find the critical path in spliced network, but also makes extension of the theory found in CPM network to spliced network becomes possible. For example, the activity total float T_ij equals to the critical path length μ^∇ minus the longest path length μ_ij^∇ through activity(ij), that is (μ^∇-μ_ij^∇); the sum of activity free float of any path μ equals to the critical path lengthμ^∇ minus the length of this path μ, that is (μ^∇-μ_ij^∇). By using these extended theory, three convenient methods are designed to detect the difference of critical and sub-critical path lengths and to find out the sub-critical path. These methods are illustrated both effective and convenient in spliced network applications.

Key words: spliced network, longest path, activity floats, CPM network