The task of assignments in project management

When describing projects and tasks, consisting of a set of sequential and interconnected operations, dynamic models are used. A network diagram is used to visually represent the structure of the projects under consideration and the interaction of work during the project. The network diagram is represented as a graph. The components of the graph are interpreted in two ways. If the vertices are events, and the arcs between them are the duration of their occurrence, in this case the problem of project management is considered. If the vertex is the work, and the arcs are the time of their execution, then the problem of finding the optimal (or critical) path is solved. In both variants of the tasks under consideration, it is important to allocate resources or performers to commit events or perform tasks. The optimality criterion for such a formulation of tasks will be an expression for calculating the total time for the execution of work. As restrictions, expressions will be used that determine the individuality of the choice of work and the assignment of performers to them, as well as the expression on the target dates for the implementation of the project in full. The total time for the execution of work and compliance with the deadlines for the implementation of the project can be considered as two main criteria for project management. This article attempts to improve the algorithm for solving the project management problem by introducing a more flexible system of weights.