|

On the Formulation of the Problem of Optimal Control of Production Parameters using a Two-Level Model of the Production Process

Авторы: Parachnevych O.О., Pihnastyi O.M. Опубликовано: 13.06.2018
Опубликовано в выпуске: #3(120)/2018  
DOI: 10.18698/0236-3933-2018-3-83-90

 
Раздел: Информатика, вычислительная техника и управление | Рубрика: Управление в социальных и экономических системах  
Ключевые слова: stability of mass production processes functioning, production systems, flow production line, enterprise, business process, basic product, technological chain, BP distribution function

Using a statistical approach, widespread in natural sciences, a two-level model to control the parameters of the flow line production system has been built. The state of the system is given by the amounts of sets of the objects of labour. The state of the subject of labour is given by a point in the phase space. The function of distribution of objects of labour by state is introduced and the kinetic equation for the distribution function is written. Now we have closed system of dynamical equations for parameters of flow production line. The null and the first moments of the distribution function of labor objects in terms of the state characterize the magnitude of interoperational stocks and the rate of processing of labor objects from operations of the technological route and are the main parameters of the management of the production line. The limiting transition from the kinetic description of the state of objects of labor to the stream description of the processing of objects of labor is accomplished. Integration of the kinetic equation by the states of the objects of labor made it possible to construct a closed system of balance equations for the parameters of the production line. The task of optimal control of the flow parameters of the production line has been set. The balance equations for the moments of the distribution function of objects of labor by states determine the constraint equations in the control problem

Литература

[1] Letenko V.A., Rodionov B.N. Organizatsiya, planirovanie i upravlenie mashinostroitelnym predpriyatiem. Vnutrizavodskoe planirovanie. Ch. 2 [Organization, planning and management of a machine-building enterprise. Intrafactory planning]. Moscow, Vysshaya shkola Publ., 1979. 232 p.

[2] Kempf K.G. Simulating semiconductor manufacturing systems: successes, failures and deep questions. Proc. 1996 Winter Simulation Conf. Institute of Electrical and Electronics Engineers, 1996, pp. 3–11.

[3] Forrester J. Industrial dynamics. Wiley, 1961. 464 p.

[4] Glushkov V.M., ed. Planirovanie diskretnogo proizvodstva v usloviyakh ASU [Planning of discrete production in the conditions of ACS]. Kiev, Tekhnika Publ., 1975. 296 p.

[5] Petrov B.N., Ulanov G.M., Goldenblat I.I., Ulyanov S.V. Teorii modeley v protsessakh upravleniya (Informatsionnyy i termodinamicheski aspekty) [Theories of models in management processes (Informational and thermodynamic aspects)]. Moscow, Nauka Publ., 1978. 224 p.

[6] Pervozvanskiy A.A. Matematicheskie metody v upravlenii proizvodstvom [Mathematical methods in production management]. Moscow, Nauka Publ., 1975. 616 p.

[7] Balashevich V.A. Matematicheskie metody v upravlenii proizvodstvom [Mathematical methods in production management]. Minsk, Vysshaya shkola Publ., 1976. 334 p.

[8] Prytkin B.V. Tekhniko-ekonomicheskiy analiz proizvodstva [Technical and economic production analysis]. Moscow, Yuniti Publ., 2000. 399 p.

[9] Pignastyi O.M. Statisticheskaya teoriya proizvodstvennykh sistem [Statistical theory of production systems]. Kharkіv, KhNU Publ., 2007. 388 p.

[10] Vlasov V.A., Tikhomirov I.A., Loktev I.I. Modelirovanie tekhnologicheskikh protsessov izgotovleniya promyshlennoy produktsii [Technological processes modeling of industrial products manufacturing]. Tomsk, TPU Publ., 2006. 104 p.

[11] Azarenkov N.A., Pignastyi O.M., Khodusov V.D. Kinetic theory of oscillations in the parameters of the production line. Dopovіdі Natsіonalnoї akademії nauk Ukraїni [Reports of the National Academy of Sciences of Ukraine], 2014, no. 12, pp. 36–43.

[12] Pignastyi O.M. The network model of the multiple resources flow manufacturing line. Nauchnyy rezultat. Informatsionnye tekhnologii [Research Result. Information technologies], 2016, vol. 1, no. 2, pp. 31–45 (in Russ.).

[13] Demutskiy V.P., Pignasta V.S., Pignastyi O.M. Teoriya predpriyatiya: ustoychivost funktsionirovaniya massovogo proizvodstva i prodvizheniya produktsii na rynok [Theory of the enterprise: stability of the mass production functioning and promotion of products to the market]. Kharkіv, KhNU Publ., 2003. 272 p.

[14] Pignastyi O.M. Analytical methods for designing technological trajectories of the object of labour in a phase space of states. Nauchnyy vestnik NGU [Scientific bulletin of National Mining University], 2017, no. 4, pp. 104–111.

[15] Pihnastyi O.M., Korsun R.O. The construction a kinetic equation of the production process. Avtomatizirovannye tekhnologii i proizvodstva [Automation of Technologies and Production], 2016, no. 1 (11), pp. 10–17.

[16] Pignastyi O.M. Engineering and production function of the enterprise with serial or mass production. Voprosy proyektirovaniya i proizvodstva konstruktsiy letatelnykh apparatov, 2005, no. 42 (3), pp. 111−117 (in Russ.).

[17] Pihnastyi O.M. Statistical validity and derivation of balance equations for the two-level model of a production line. Skhіdno-Єvropejskij zhurnal peredovih tekhnologіj [Eastern-European Journal of Enterprise Technologies], 2016, vol. 5, no. 4 (83), pp. 17–22.

[18] Demutskiy V.P., Pignasta V.S., Pignastyi  O.M. Stochastic description of economic-production systems with mass production. Dopovіdі Natsіonalnoї akademії nauk Ukraїni [Reports of the National Academy of Sciences of Ukraine], 2005, no. 7, pp. 66–71.

[19] Moiseev N.N. Elementy teorii optimalnykh system [Elements of the optimal systems theory]. Moscow, Nauka Publ., 1974. 526 p.

[20] Pignastyi O.M., Khodusov V.D. Model of conveyer with the regulable speed. Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie [Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming & Computer Software], 2017, vol. 10, no. 4, pp. 64–77. DOI: 10.14529/mmp170407

[21] Armbruster D., Marthaler D., Ringhofer C., Kempf K., Jo T.-C. A continuum model for a re-entrant factory. Operations Research, 2006, vol. 54, no. 5, pp. 933–950. doi: 10.1287/opre.1060.0321