In this study, it is aimed to develop a new type mathematical model to obtain optimal planning and scheduling with the minimum project cost for construction project and a new type network planning and scheduling model for solving optimal resource allocation problem through determining total amount allocated to construction project is developed as follows: At first stage an optimal scheduling problem with the minimum idle cost consumed by operations of construction resources is formulated through the topological analysis based on the theory of graph and network structure. After formulating scheduling model a mathematical model formulation and an algorithm to solve it effectively is established from the different viewpoint from existing PERT-type network planning scheduling method based on the analysis of topological characteristics of construction project network. At the second stage the scheduling model formulated above is transformed to equivalent optimization model formulated utilizing the cut set structure and the route set structure, and an effective algorithm is developed adopting DP procedure in which the algorithm is established as optimal resources allocation problem in cut-network which is transformed topologically from original project network.