Algorithm for solving multicriteria problem of appointments on the networks

To describe complex projects or various jobs that make up a set of interrelated activities, use the network schedule. Several variants of network models are used. 1. For practical use, the Gantt chart is the most widely used - it is a graphical representation of consecutive intervals of time and the use of resources. 2. The network graph is represented as a graph, where the vertices are an event (or its state at a certain point in time), and the connecting arcs (or edges) are works. The graph model is used in the work. In this case, the events (the fact of the completion or the beginning of the work) correspond to the vertices of the graph, and the work to the arcs, the orientation of which corresponds to the technology of this process. An important role in the project management model is played by the optimal assignment of performers to the existing list of works. With this formulation of the problem, the total implementation time or the length of the critical path on the graph can be used as a criterion. In this case, the criterion is imposed a restriction on the deadline for the execution of work (or the project as a whole). Thus, the total time spent on the project and the length of the critical path are represented by equally important characteristics of the project implementation, and they should be considered as two equivalent criteria for the multicriteria project management task. We have proposed an algorithm, in general, an approximate determination of the set of Pareto-optimal solutions of a given problem.