Selection of alternative solutions in the optimization problem of network diagrams of project implementation

The object of research is a model network diagram of the project implementation in the form of a diagram, in which individual operations are represented by arcs, and vertices are considered as events corresponding to the beginning and end of operations. The term «model» is understood as an arbitrary network diagram, in relation to the parameters of which the solution is already known. One of the most problematic areas is the lack of substantiated methods of formalizing the task of optimizing network diagrams, allowing for a targeted selection of early start dates for individual operations within the project, ensuring optimal solutions for the selected criteria. In this study, such criteria are the possibility of shifting the operation with the maximum intensity in a given time interval, and the uniformity of the workload of personnel, assessed by the ratio of the maximum and minimum intensities y=qmax/qmin for the analyzed version of the network diagram. Methods of network planning and management, mathematical experimental planning and optimization methods are used. The results obtained confirm the possibility of using the proposed methods for solving optimization problems with respect to arbitrary network diagrams. This is due to the fact that the proposed methods for optimizing network diagrams allow one to obtain regression equations that serve as mathematical models for making targeted decisions on the choice of early start dates for operations that provide the best results in relation to the selected optimization criteria for network diagram. The features of the proposed solutions are: conditions for the selection of input variables, a procedure for the targeted selection of early start dates for operations with the highest load intensity of personnel, and providing optimal solutions for the criterion of minimizing uneven load. Thanks to these features, it is possible to optimize network diagrams with arbitrary source data. To do this, it is enough to apply the proposed procedure for your version of the network diagram, having previously estimated possible alternatives with respect to the choice of significantly influencing input variables and the intervals of their variation.