Purpose of the study. The problem of determining the rating of an expert is considered. In this case, the rating will be determined by the results of the last discussion, that is, the assessment of the i-th expert will depend on the assessment that he received as a result of this discussion. Relationships in such a community are proposed to be described using an interaction graph. It is shown that this interaction graph will be described by the Kirchhoff matrix, which has a determinant equal to zero and a rank one less than the dimension of the Kirchhoff matrix. Materials and methods. Thus, to solve the problem posed, it is required to find a solution to a homogeneous system of equations whose matrix is the Kirchhoff matrix. It is proposed to use an algorithm that can be applied without numerous intermediate transformations, but it is required to carry out the operation of inverting the original matrix of a sufficiently large dimension. This appears to be a rather labor intensive operation. That is why it is proposed to use the Tikhonov regularization method, which allows replacing the solution of the original problem with the problem of minimizing the Tikhonov functional. Such a replacement leads to the problem of the complexity of the solution of which is also significant. Therefore, taking into account the property of the problem being solved, when it is necessary to obtain not the absolute value of the rating, but a system of ratings that reflect the relative importance of each expert in relation to each other, an approximate algorithm for solving the problem is proposed when the value of the regularizing parameter is selected during iterations. Results. An example is considered for the case of five experts, the matrix of interaction between the participants of this expert community is given in the form of a table. The above algorithm makes it possible to assess the competence of experts quite accurately and precisely for a specific situation, taking into account the opinion of the entire expert community. Next, we consider the case when there is information about the initial rating of each of the experts. Focusing on the fact that in order to solve the problem it is necessary to find not the absolute value of the rating of each expert, but only the ratio between the ratings, we arrive at an algorithm that allows us to move from a homogeneous system of equations to a heterogeneous one, thereby bypassing the need to invert a large-dimensional matrix. Conclusion. An algorithm for solving the problem of constructing a rating estimate for two cases is considered: there are no initial estimates of the competence of specialists and the case when there is information about the initial rating of each of the experts.
Logistics in the field of construction is one of its most important components, directly affecting the success of the implementation of construction projects. The problem of the optimal distribution of available limited resources is an important and urgent task in planning and organizing construction work, especially in conditions of scarcity of resources. The solution of this problem directly affects the quality and result of construction projects, the duration and rhythm of construction, costs and labor productivity. Aim. The purpose of the study is to develop a mathematical model based on vector optimization methods that allows optimal distribution of various types of limited resources between construction activities, works or objects in order to increase the efficiency of construction projects. Materials and methods. The model of resource distribution described in the paper is based on the theory of vector linear optimization, which makes it possible to distribute limited resources of various types between works, activities, or construction objects. The model takes into account the minimum and optimal requirements for providing construction objects or works with resources, their supply, as well as the priority for supplying objects. A technique for organizing computational procedures according to the model by numerical methods is given. Simulation methods based on computational experiments substantiate the adequacy of the proposed model and the properties of the results obtained from it. Also, the effectiveness of the implementation of the resource allocation model in the system of planning and management of construction projects was assessed. Results. A mathematical model for the distribution of limited resources between construction objects, works or events has been developed and justified. The adequacy of the results obtained by the model is proved. A technique for carrying out computational procedures for the numerical implementation of the model in the MS Excel environment is described. On the basis of computational experiments, the efficiency of applying the resource allocation model in the management of construction projects was evaluated, which averaged more than 34%. Conclusion. The relevance of developing a model for the distribution of resources of various types in the field of construction is shown, the adequacy of the results is proved, the method for obtaining estimates from the model by numerical methods is described, and the economic effect of applying the model in practice is estimated. The proposed resource allocation model leads to a significant increase in the efficiency of organization and management of construction projects and increases the likelihood of their timely completion at minimal cost.
The purpose of the study. The process of enterprise development involves the implementation of a sequence of projects, each of which has its own life cycle. One of the main tasks of the company's management is to provide conditions for each of the projects to start paying off. Given the fact that modern projects, as a rule, have a fairly long implementation period, it should be recognized that the decision to implement the project in full will probably not be the most optimal. As a rule, in this case, they prefer to divide the project into stages or, as is customary in industrial construction, into queues. Materials and methods. The formal statement of the tasks defining: the minimum number of basic representatives, minimization of terms of preparation of production of new types of equipment and minimization of time of production of basic representatives of new equipment is given. For cases of small dimension of the problem, an exact algorithm based on a complete search of options is proposed. For the case of large-dimensional problems, a compositional algorithm is proposed, which consists in dividing the entire set of products into several subsets, to each of which an exact algorithm is applied. Results. The algorithms considered are based on a threshold scheme for solving an optimization problem, when a threshold value of the creation time of one of the products is introduced, which will coincide with one of the components of the vector that sets the standard creation time of each of the products. In this case, iterative and decomposition algorithms can also be used. The case of solving this problem as a problem of partial covering of a bipartite graph is considered separately. An algorithm for obtaining a lower estimate of the problem based on the network programming method is given. Conclusion. The analysis was carried out and the procedure for selecting the basic products of a new generation of equipment was developed, which allows, depending on the conditions set by the decision-maker (LPR), to determine the basic product of the technology direction that most fully corresponds to the functional, constructive and technological features of the generation of equipment.
Accounting for possible risks that affect the successful implementation of construction projects is one of the most important tasks in planning and managing construction. The main problem for risk accounting is that they arise under the influence of random factors under conditions of high uncertainty. Therefore, the vast majority of risk accounting methods in construction are based on probabilistic models. Given the fact that recently the level of uncertainty in almost all areas of economic activity has increased significantly, it is necessary to develop new approaches to risk analysis that would respond as accurately and quickly as possible to emerging threats. Aim. The purpose of the study is to develop a mathematical model based on the theory of random Markov processes, which allows, in a probabilistic approach, to analyze the negative impact of adverse factors on the implementation of construction projects in the dynamics of their receipt under conditions of high uncertainty in order to increase the efficiency of construction work. Materials and methods. The risk assessment model of the influence of unfavorable factors on a construction project, presented in the paper, is based on the theory of Markov random processes, which makes it possible to assess the probability of the implementation of possible threats with varying degrees of damage, and to calculate risks during construction work. The model assumes that threats that cause different levels of damage to a construction project arrive at random times and require different times to eliminate them. To implement the model, a system of differential equations is given, which is solved by numerical methods. An analysis of the solution under various conditions of threats is carried out. The influence of negative factors on the construction project during its long-term implementation is considered separately. The analysis of the influence of temporal and probabilistic parameters of the task on the degree of risks in the implementation of construction projects was carried out. Results. The relevance of developing a risk assessment model for the implementation of construction projects is shown, goals and objectives for scientific research are set. The ways of solving the set tasks are given and substantiated. A mathematical model has been developed that makes it possible to estimate the probabilities of finding a construction project in various states, differing in different degrees of risk during the implementation of the project. On the basis of numerical methods, the practical implementation of the model is given for various parameters characteri¬zing the influence of negative factors on the progress of the construction project. The results of the practical implementation of the model are analyzed, recommendations are given for using the model in practice. Conclusion. The presented dynamic risk assessment model for the implementation of construction projects can serve as the basis for building an optimal control system for the progress of construction work and making decisions on the organization of construction activities.
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