This article proposes an optimization model for preventing the waste of time in the educational and research activities' cycle of an organization such as a university. For this purpose and in order to increase efficiency and prevent the waste of time; the graph theory models have been used. The educational and research activities diagrams of a supposed university is drawn by the use of graphs theory model, and then these graphs are analyzed, then in order to design a model, the units, activities and the time of doing each activity are symbolized, and the collected data are presented in the form of matrix. In this article two procedures are suggested for optimization; using subgraphs for every activity cycle in order to shorten the activity cycles and minimizing the time of doing each work. The algorithm of time minimizing is based on recognizing and determining the edges with the most weight as the maximum time. Also the influential factors on the waste of time in activity cycle are recognized and then replaced or omitted.