Multiple-Model Description and Control Construction Algorithm of Supply Chain

  • Inna Trofimova
  • Boris Sokolov
  • Dmitry Ivanov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 765)


In this paper a multiple-model description of supply chain (SC) is presented. The SC state change is described through differential equations based on a dynamic interpretation of the job execution. The problem is represented as a designing control of SC problem in presence of external actions. The approach is based on decomposition of the problem on two parts and its solution with the help of optimal control theory methods and linear programming.


Models of supply chain Optimal program control Positional control 



The research described in this paper is partially supported by the Russian Foundation for Basic Research (grants 16-07-00779, 16-08-00510, 16-08-01277, 16-29-09482-fi-i, 17-08-00797, 17-06-00108, 17-01-00139, 17-20-01214, 17-29-07073-fi-i, 18-07-01272, 18-08-01505), grant 074-U01 (ITMO University), state order of the Ministry of Education and Science of the Russian Federation 2.3135.2017/4.6, state research 007320180003, International project ERASMUS +, Capacity building in higher education, 73751-EPP-1-2016-1-DE-EPPKA2-CBHE-JP, Innovative teaching and learning strategies in open modelling and simulation environment for student-centered engineering education.


  1. 1.
    Schwartz, D., Wang, W., Rivera, D.: Simulation-based optimization of process control policies for inventory management in supply chains. Automatica 125(2), 1311–1320 (2006)CrossRefzbMATHGoogle Scholar
  2. 2.
    Garcia, C.A., Ibeas, A., Herrera, J., Vilanova, R.: Inventory control for the supplychain: an adaptive control approach based on the identification of the lead-time. Omega 40, 314–327 (2012)CrossRefGoogle Scholar
  3. 3.
    Perea, E., Grossman, I., Ydstie, E., Tahmassebi, T.: Dynamic modeling and classical control theary for supply chain management. Comput. Chem. Eng. 24, 1143–1149 (2000)CrossRefGoogle Scholar
  4. 4.
    Ortega, M.: Control theory applications to the production-inventory problem: a review. Int. J. Prod. Res. 8(2), 74–80 (2000)Google Scholar
  5. 5.
    Ivanov, D., Sokolov, B., Solovyeva, I., Dolgui, A., Jie, F.: Dynamic recovery policies for time-critical supply chains under conditions of ripple effect. Int. J. Prod. Res. 54(23), 7245–7258 (2016)CrossRefGoogle Scholar
  6. 6.
    Ivanov, D.A., Sokolov, B.V.: Adaptive Supply Chain Management. Springer, Wiley and Sons, New York (2010)CrossRefGoogle Scholar
  7. 7.
    Kalinin, V.N., Sokolov, B.V.: Optimal planning of the process of interaction of moving operating objects. Int. J. Differ. Equations 21(5), 502–506 (1985)zbMATHGoogle Scholar
  8. 8.
    Chen, Z.L., Pundoor, G.: Order assignment and scheduling in a supply chain. J. Oper. Res. 54, 555–572 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Gubarev, V.A., Zakharov, V.V., Kovalenko, A.N.: Introduction to systems analysis. LGU, Leningrad (1988)Google Scholar
  10. 10.
    Chernousko, F.L.: State Estimation of Dynamic Systems. SRC Press, Boca Raton (1994)zbMATHGoogle Scholar
  11. 11.
    Gabasov, R., Dmitruk, N.M., Kirillova, F.M.: Numerical optimization of time-dependent multidimensional systems under polyhedral constraints. Comput. Math. Math. Phys. 45(4), 593–612 (2005)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Solovyeva, I., Ivanov, D., Sokolov, B.: Analysis of position optimization method applicability in supply chain management problem. In: 2015 International Conference on “Stability and control processes” in memory of V.I. Zubov, pp. 498–500 (2015)Google Scholar
  13. 13.
    Popkov, A.S., Baranov, O.V., Smirnov, N.V.: Application of adaptive method of linear programming for technical objects contro. In: 2014 International Conference on Computer Technologies in Physical and Engineering Applications ICCTPEA 2014 - Proceedings, p. 141 (2014)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.St. Petersburg Institute for Informatics and Automation of the Russian Academy of SciencesUniversity ITMOSt. PetersburgRussia
  3. 3.Berlin School of Economics and LawBerlinGermany

Personalised recommendations