Cybernetics and Systems Analysis

, Volume 54, Issue 5, pp 744–753 | Cite as

Optimal Control Problem for a Conveyor-Type Production Line

  • O. M. Pihnastyi
  • V. D. Khodusov


A method is developed for the optimal control of parameters of a conveyor-type production line. The model of the conveyor line is presented by the partial differential equation, which allows taking into account the distribution of products along the technological route as a function of time. Various variants of stepped speed control of the conveyor belt are investigated. The features of stepped control are described. The divergence of the rate of output by the production line from the given demand is determined for different parameters of stepped control.


conveyor subject of labor production line parameters of the state of production line technological position transition period production management systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A.M. Law, Simulation Modeling and Analysis, McGraw-Hill, New York (2015).Google Scholar
  2. 2.
    D. Gross and C. M. Harris, Fundamentals of Queueing Theory, Wiley, New York (1985).zbMATHGoogle Scholar
  3. 3.
    A. Grosler, J. H. Thun, and P. M. Milling, System dynamics as a structural theory in operations management, Production and Operations Management, Vol. 17, No. 3, 373–384 (2008).CrossRefGoogle Scholar
  4. 4.
    O. M. Pihnastyi, A new class of the dynamic models of production lines of production systems, Sci. Bulletin of Belgorod State University, No. 31/1, 147–157 (2014). DOI:
  5. 5.
    E. Lefeber, R. A. Berg, and J. E. Rooda, Modeling, validation and control of manufacturing systems, Proc. 2004 American Control Conference, Boston (2004), pp. 4583–4588. DOI:
  6. 6.
    D. Armbruster, C. Ringhofer, and T.-J. Jo, Continuous models for production flows, Proc. 2004 American Control Conference, Boston (2004), pp. 4589–4594.Google Scholar
  7. 7.
    U. S. Karmarkar, Capacity loading and release planning with work-in-progress (WIP) and leadtimes, J. of Manufacturing and Operations Management, No. 2, 105–123 (1989).Google Scholar
  8. 8.
    V. P. Demutskii, V. S. Pihnastaya, and O. M. Pihnastyi, Stochastic description of economic–production mass output systems, Dopov. Nac. Akad. Nauk Ukr., No. 7, 66–71 (2005). DOI:
  9. 9.
    R. Berg, E. Lefeber, and J. Rooda, Modelling and control of a manufacturing flow line using partial differential equations, IEEE Trans. on Control Systems Technology, Vol. 16, No. 1, 130–136 (2008). DOI: Scholar
  10. 10.
    M. La Marca, D. Armbruster, M. Herty, and C. Ringhofer, Control of continuum models of production systems, IEEE Trans. on Automatic Control, Vol. 55, No. 11, 2511–2526 (2010). DOI: Scholar
  11. 11.
    R. M. Colombo, M. Herty, and M. Mercier, Control of the continuity equation with a non-local flow, ESAIM: Control, Optimisation and Calculus of Variations, Vol. 17, No. 2, 353–379 (2011). DOI: Scholar
  12. 12.
    S. Steffensen, S. Steffensen, M. Herty, and L. Pareschi, Numerical methods for the optimal control of scalar conservation laws, IFIP Conf. on System Modeling and Optimization, Springer, Berlin–Heidelberg (2011), pp. 136–144. DOI: Scholar
  13. 13.
    M. Bambach, A.-S. Häck, and M. Herty, Modeling steel rolling processes by fluid-like differential equations, Applied Mathematical Modelling, Vol. 43, 155–169 (2017). DOI: 10.056.Google Scholar
  14. 14.
    D. Armbruster, D. Marthaler, C. Ringhofer, K. Kempf, and T. C. Jo, A continuum model for a re-entrant factory, Operations Research, Vol. 54, No. 5, 933–950 (2006). DOI: Scholar
  15. 15.
    C. D’Apice, P. I. Kogut, and R. Manzo, On optimization of a highly re-entrant production system, Networks and Heterogeneous Media, Vol. 11, No. 3, 415–445 (2016). DOI: Scholar
  16. 16.
    V. P. Demutskii, V. S. Pihnastaya, and O. M. Pihnastyi, Theory of an Enterprise: Sustainable Operation of Mass Production and Production Promotion on the Market [in Russian], KhNU, Kharkiv (2003). DOI: 10.13140/RG.2.1.5018.7123.Google Scholar
  17. 17.
    O. M. Pihnastyi, Problem of optimal operating control of macroparameters of a mass output production system, Dopov. Nac. Akad. Nauk Ukr., No. 5, 79–85 (2006). DOI: 10.13140/RG.2.2.29852.28802.Google Scholar
  18. 18.
    V. Ya. Zaruba and O. M. Pihnastyi, Engineering content and statement of the problem of program control in parameters of the production line with the use of overtime works, in: Control in Engineering, Ergatic, Organizational, and Network Systems: A Collection of Papers of 5th Russian Multiconference on Control Problems ITU-2012, October 9–11, 2012, St.-Petersburg, TsNII Elektroinstrument, (2012), pp. 576–579. DOI:10.13140/RG.2.2.30481.43364.Google Scholar
  19. 19.
    D. Armbruster and R. Uzsoy, Continuous dynamic models, clearing functions, and discrete-event simulation in aggregate production planning, Tutorials in Operations Research: New Directions in Informatics, Optimization, Logistics, and Production (2012), pp. 103–126. DOI: Scholar
  20. 20.
    SIMINE for conveyors. Siemens. 2017. URL: (accessed 12 April 2017).
  21. 21.
    A. K. Semenchenko, N. I. Stadnik, P. V. Belitsky, D. A. Semenchenko, and E. Yu. Stepanenko, Influence of the non-uniformity of the load of a belt conveyor on the load of driving engines and energy consumption for transportation, The East European J. of Advanced Technologies, Vol. 4, No. 1 (82), 17–22 (2016). DOI: Scholar
  22. 22.
    V. P. Kondrakhin, N. I. Stadnik, and P. V. Belitsky, Statistical analysis of operational parameters of a mine belt conveyor, Naukovi Pratsi DonNTU, Ser. Elektromekhanichna, No. 2 (26), 140–150 (2013).Google Scholar
  23. 23.
    V. N. Prokuda, Yu. A. Mishanskii, and S. N. Protsenko, Analysis and estimate of traffic flows on the turnpike conveyor carrier PSP mine Pavlogradskaya PAO DTEK Pavlogradugol, Gornaya Elektromekhanika, No. 88, 107–111 (2012).Google Scholar
  24. 24.
    Bartec (2017). URL: (accessed 12 April 2017).

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Technical University “Kharkiv Polytechnic Institute”KharkivUkraine
  2. 2.V. N. Karazin Kharkiv National UniversityKharkivUkraine

Personalised recommendations