Abstract
When planning projects, events, work packages, it is always necessary to take into account the influence of internal conditions and the external environment. In most cases, the influence of external factors on the project is stochastic and is a random process. Scientific developments allowing to take into account the influence of the external environment on the development and implementation of projects are always relevant, since they will allow to predict the temporal characteristics of projects in real conditions. Aim. In scientific research, the task is to develop a mathematical model that allows dynamics to predict the temporal performance of projects, taking into account the influence of random external factors on them. Materials and methods. It is possible to solve the problem by describing the process of the influence of external factors on the project by mathematical methods of the theory of Markov random processes. At the same time, factors affecting the project are conditionally divided into those that lead to the need for additional activities in the development of projects, and to factors that require a fundamental change in the project. In a scientific study, mathematical methods of probability theory, the theory of differential equations, and numerical methods are used. Results. Based on the theory of Markov random processes, a dynamic model for the development and implementation of the project was developed taking into account the influence of external random factors on these processes. A methodology for the formation and solution of a mathematical model is described, which allows one to find the time dependences of the probabilities of completion of individual stages of project development and the probability of successful implementation of the project as a whole. The analysis of the solutions obtained is carried out, general trends in the development and implementation of projects are described taking into account the influence of external factors on them. Conclusion. The presented model makes it possible to evaluate the probabilities of the project in general and of its individual stages for different time intervals, which will allow you to plan timelines for project management. The model can complement the network planning and management procedures and provide additional probabilistic estimates of the project time.
Highlights
Постановка задачи и ее математическая модельРассмотрим некоторый проект, который необходимо реализовать в будущем, и определим весь цикл его разработки и реализации, начиная с самого раннего момента принятия решений об осуществлении проекта
When planning projects, events, work packages, it is always necessary to take into account the influence of internal conditions and the external environment
Scientific developments allowing to take into account the influence of the external environment on the development and implementation of projects are always relevant, since they will allow to predict the temporal characteristics of projects in real conditions
Summary
Рассмотрим некоторый проект, который необходимо реализовать в будущем, и определим весь цикл его разработки и реализации, начиная с самого раннего момента принятия решений об осуществлении проекта. 2, продолжительность этапа начала разработки проекта быстро приближается к нулю, вероятности состояний с проведением дополнительных мероприятий и процесса принятия решений о реализации проекта имеют экстремумы, а вероятность выполнения проекта в общем монотонно стремится к единице, что согласуется с поставленной задачей. 3. Временные зависимости вероятности выполнения проекта при разных значениях параметра T3 (T1 = 3 дня, T2 = 5 дней, T4 = 12 дней, р = 0,5). 4. Временные зависимости вероятностей выполнения проекта при разных значениях параметра T4 (T1 = 3 дня, T2 = 5 дней, T3 = 15 дней, р = 0,5). 5. Временные зависимости вероятности реализации проекта при разных значениях параметра р (T1 = 3 дней, T2 = 5 дней, T3 = 15 дней, T4 = 12 дней). Представленная модель позволяет оценивать вероятности выполнения проекта как в общем, так и отдельных ее этапов для разных временных интервалов, что позволит планировать времен-.
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