Abstract: The object of research in the work involves the complex service systems, which are characterized by mutual dependence between the works, their random duration and necessity of rationalize recourses in time. These features stipulate the development of a mathematical model which is meant to form the basis for the optimization task of forming a schedule. As the objective function, a generalized criterion that allows the most efficient allocation of resources over time is chosen. An important parameter of this model is the duration of the service. The assessment of this parameter is an important task, since it directly affects the accuracy of the developed schedule.The formation of a mathematical model is based on the apparatus of probability theory and the theory of project management. To find the duration of the service a cubic equation connecting the variance, the expectation and the mode of the cubic equation was obtained. As a result a mathematical model a mathematical model designed for describing multi-stage servicing systems with a stochastic duration of maintenance of mutually dependent works was found by the authors. This model may be used to describe a whole class of systems with the above features in the case where it is necessary to efficiently allocate resources  over time. Novelty is present in the use of a generalized resource criterion in conjunction with resource and time constraints. The author also finds an evaluation of service time, which is distinguished by increased accuracy in comparison with existing analogues.

Abstract: This article examines the task on optimization of the process of freight transports from the perspective of maximization of the profit. The object of this research is the material and corresponding to them financial flows emerging in delivering of the incoming orders. The subject of this research is the coordination of actions on managing the process of selection of an order by transportation means in large volume transports. The goal of the work consists in formulation of the approach, which allows optimizing the process of freight transports considering the current status and load of the transport from the perspective of maximization of the gained profit. The authors suggest a multi-agent approach as a method of solution of the set task. Each of the intellectual agents of the system resolves the task of purposefulness of receiving the order based on the assigned by it transportation means. As a result, the authors propose a mathematical model of the system, which takes into account the current status of transportation means, their capacity, and the ability of execution of the same order by multiple transports. The scientific novelty consists in development of the structure of multi-agent system with clarification of the key functions of the agents alongside the description of specificity of their interaction.

Abstract: The subject of the research in this paper is the probability density function (PDF) of the random variable, which is the sum of a finite number of beta values. This law is widespread in the theory of probability and mathematical statistics, because using it can be described by a sufficiently large number of random events, if the value of the corresponding continuous random variable concentrated in a certain range. Since the required sum of beta values can not be expressed by any of the known laws, there is the problem of estimating its density distribution. The aim is to find such approximation for the PDF of the sum of beta-values that would have the least error. To achieve this goal computational experiment was conducted, in which for a given number of beta values the numerical value of the PDF with the approximation of the desired density were compared. As the approximations it were used the normal and the beta distributions. As a conclusion of the experimental analysis the results, indicating the appropriateness the approximation of the desired law with the help of the beta distribution, were obtained. As one of the fields of application of the results the project management problem with the random durations of works is considered. Here, the key issue is the evaluation of project implementation time, which, because of the specific subject area, can be described by the sum of the beta values.

Abstract: The objects of the research are the complex service systems, the distinctive feature of which is the stochastic duration of the servicing of the complex of mutually dependent works that define the project. The aim of the work is to develop a schedule of service requests taking into account restrictions on the time of service and on the amount of resources. As an optimization criterion a generalized resource criterion is selected. This criterion allows describing such modes as uniform system load, maximum load, etc depending on the preferences of the user. Methods of building the schedule are based on the numerical algorithms, which are formed with the help of heuristics. This heuristics are determined by the analysis of the existing approaches and specific objectives of the study. As a result the study proposes a complex of numerical methods that constitute the basis of the software for building the schedule service applications. The novelty of the study consists in the application of heuristics that provide a suboptimal schedule in a reasonable time. As one of the applications of the results the article shows the optimization of functioning of the wagon repairing production.

Abstract: In this paper the problem of project management with the random duration of works is considered. An important task is to analyze the risk of delayed completion of such projects. Existing approaches are based on assumptions that are not always feasible under real conditions. In this regard, it is necessary to develop mechanisms for research on the accuracy of the available estimates and may modify them. The object of study is a project given a set of mutually-dependent work with random time of execution. Object of research is probabilistic-temporal characteristics of such project. The aim of the study is to obtain a probability-time characteristics through a series of experiments. To achieve this goal it is necessary to design and implement a system simulation, which allows taking into account the specifics of the problem to conduct experiments to analyze the characteristics of the project. As a result, a system simulation is proposed, which is a fundamental difference from existing analogues is to focus on the use of solutions for a class project management tasks with random duration of execution of certain works. The system allows the researcher to conduct a variety of experiments to obtain the statistical characteristics of the duration of the project in different conditions.

Abstract: In this paper a problem of network planning and management with a random duration of individual operations is considered. The subject of the study is the law of distribution of the random variable which describes duration of the project. The aim is to estimate such law. The urgency of this problem is related to the need to improve the accuracy of the known existing assessments which do not take into account the specifics of the distribution law of separate works determining the project. The main difficulty of the practical solution of this problem is the need to calculate the multiple definite integral, wherein the number of individual integrals not known in advance and determined by the number of works that make up the critical path of the project. As a result, the numerical method based on recursion is proposed, which allows to numerically estimate the desired distribution law. Scientific novelty of the results is in obtaining estimates of the distribution law of the duration of the project that improves positional accuracy over the existing analogues. Without loss of generality developed a recursive algorithm can be used for a wide class of problems in which the unknown distribution of the sum of random variables with known distributions of the individual terms.