There is a wide class of planning tasks in which possible technologies of works execution and their combinations can be succeeded by the alternative variants. These variants can be represented as network models. The dependence between scope, time and cost of works execution are discrete. The goal of work is to creat effective methods for these tasks solution. The mathematical models and minimization method of project execution time on the project with possible funding constrains during different periods and with given alternative variants of the network models fragments are offered in this paper. For project cost minimization problems solution the mathematical model and minimization method of project works costs with project works execution terms constraints and given alternative variants of the network models fragments are offered
