mathematical models

Introduction. The majorityof projects implemented in the world community exceeds in duration and cost limits indicated on the planning phase, so they are not successfully executed. In our opinion, the main reason for this situation is the complexity of the optimal selection and appointment of executors to perform main project work, coupled with the lack of consideration for a number of important factors. Theoretical analysis. Theory and practice of project management and operations research proposed a number of optimization models for drafting work schedules taking into account their interrelationships, as well as the necessary resources. These models are usually referred to a class of extremely NP-hard, which explains some difficulties for their effective implementation into practice. Methodology. The basic problem of optimal selection and executors’ appointment for project work, which takes into account the topology of the network schedule, as well as the optimization criterion serving the duration of the project is researched. In researched model the limits on the total cost of all the work for the project are set, and it is determined that only one executor is involved for each job, which, if necessary, is able to perform a number of tasks. Results. During the research more significant limitations, which are implemented in the model and can significantly expand the scope and improve the efficiency of its use in practice, were developed by authors. The article provides a detailed description of the meaningful data limitations, as well as their correct formalization.