Mathematical modeling of multystage technological process

Аuthors

Kozelkov O. A.

Scientific-production enterprise «Kant», 12/7, Talalikhina str., Moscow, 109316, Russia

e-mail: kozelkov@pochta.ru

Abstract

Subject of study in the article are models and methods of analysis and evaluation of functional parameters of successive line production process. The aim is to assess the technological feasibility of the planned production processes through the analysis and consideration of the characteristics of individual process steps and equipment used.
Tasks it is been: ground of expedience of application of mass service theory for the mathematical design of technological processes; development of model of the queuing system, describing successive technological processes for the receipt of functional and cost descriptions of production; determination of mathematical expressions for the receipt of cost descriptions of production processes with the purpose of determination of equipment composition for providing of the set productivity and necessary amount of the same type equipment.
In-use methods are a mathematical design on the basis of theory of mass service, in particular are probabilistic models of the multiphase queuing system.
Following results were obtained. It is shown that, when assessing the feasibility of the planned production of the manufacturing process it is advisable to use mathematical modeling, since it is possible to determine the qualitative and quantitative characteristics of equipment and tools, based on which the analysis is made possible TP and rating them on the specified criteria, such as cost, time, volume release and other. The mathematical expressions for the main characteristics that define the state of the production system as a multiphase queuing system are obtained. The integral characteristics of production, such as the average &amount of work in progress and the average cycle time are determined. The cost queuing model aimed at determining the optimal level of functioning of the production system is given. The steps of method for determining cost characteristics of processes are proposed on the based on the above models.
Conclusion. Thus, we obtain the possibility to simulate the stream processes of modern production and evaluate the time and cost parameters for the feasibility analysis of requirements in the development plans of production. The results can be used in the development of information technology and automation tools for the planning and control of production processes.

Keywords:

modeling of the production process, a multi-stage technological process, multiphase queuing system.

References

1. Kleinrok L. Teoriya massovogo obsluzhivaniya (Queueing Theory), Moscow, Mashinostroenie, 1979, 432p.
2. BilikR.V., Myasoedova Z.P., Petukhova N.V., Farkhadov M.P. Inzhenernye metody rascheta setei pri proektirovanii raspredelennykh avtomatizirovannykh sistem massovogo obsluzhivaniya (Engineering calculation methods for the design ofdistributed networks ofautomated queuing systems), Moscow, MAKS Press, 2010, 256p.
3. Ivanov A.A. Trudy NGTU, 2013, no.1, pp. 88-93.
   
4. Ivlev M.A. Voprosy sovremennoi nauki ipraktiki, 2009, no.6, pp. 23-28.
   
5. Gogin A.A., Solon B.Ya. Sovremennye naukoemkie tekhnologii, 2010, no.1, pp. 21-26.