Mathematical formulation of the problem of modeling the flow organization of works in construction
Authors: Sokolnikov Vladimir V. 
Published: April 2020

Introduction. Improving the efficiency of research in the field of оrganisation of construction requires the development of a deterministic model of the flow organization of work. Development of the specified model will allow to improve methods of development of POC and PPR providing organizational and technological reliability of construction both at the stage of project preparation, and in the main period of construction. The purpose of this article is a mathematical formulation of the problem of modeling the flow organization of construction works. The object of the study is the parameters of a deterministic mathematical model of the flow organization of works performed in a given period of time (day) in the allocated part of the construction volume of the structure.
Materials and methods. The hypothesis of the proposed method of modeling the process of building construction is that the change (increment) of the construction readiness of the structure (change in the “up” direction of mass, shape and position of the assembled structures) can be expressed, according to the representations of mathematical physics, through the speed of movement of the masses of material objects (construction flow) arising as a result of the application of forces (technological flow) acting for a certain period of time, in the aggregate, forming a physical environment “flow of flow in time and space” masses of materials from the initial (stored) position in the finished construction products in the design marks. The mass of elements, their distribution in space, the mass of the structure in parts and in General (collection of loads) is determined at the design stage, including according to BIM models. Analysis from this standpoint the equations of the mechanics of fields of force distribution applied to the problem of the study organization of the “flow” of work on the private front will assess the prospects for the proposed hypotheses for the construction of approximate deterministic models of organization of construction, based on concepts of physics.
Results. Mathematical model of production organization of construction works on the basis of physical representations of technological processes as a “stream flowing through time and space” of the masses of the materials from the initial (stored) position in finished building products in the project level under the influence of applied forces explicitly establishes the dependence of the change in the value of construction completion of construction parameters of the process flow. To obtain numerical values of boundary conditions for the construction readiness function, the development of algorithms for processing BIM data arrays will be required. To determine the initial conditions of the parameters of the technological flow vector that satisfy the dimension obtained in the article, it will be necessary to develop special algorithms and their software.
Conclusions. Using the proposed physical model of flow of organization work (model building flow) in the perspective automated systems of designing of construction will allow in the period of the CMP to analyze their progress based on a variant of the estimated forecasts of changes in construction readiness of the facility for the monitoring period of time and under different set parameters of the vector — potential of the process flow, which in turn, ensures organizational — technological reliability of construction by technical means of timely and reliable operational management.