The task of operational management of the projects

We consider the problems of operational management of projects. The tasks are to reduce the completion date of the project to the desired value with minimal cost. It is assumed that for each job there is the variant of reducing its duration. An efficient algorithm for solving the problem for the case when cost functions are discrete, for a network graph with tree view, and for the aggregated networks is suggested. Theorems about necessary and sufficient conditions in order that the network graph has been aggregated, about the lower evaluation for the original problem and the reduction of the problem of the variables choice maximized the lower bound to the problem of convex programming are proved. For the general case of the method of branches and borders with obtaining of the estimates based on the method of network programming is suggested.