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The Stackelberg Model in Territorial Planning

  • Control in Social Economic Systems
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Abstract

We propose a new model for the formation of a public-private partnership mechanism, formulated as a bilevel Boolean programming problem. We show that this task is ∑ P2 -hard in both optimistic and pessimistic forms. We develop a stochastic iterative algorithm for solving this problem. We also present computational experiments on real information that demonstrate the capabilities of the proposed approach.

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References

  1. Ereshko, F.I., Modelirovanie refleksivnykh strategii v upravlyaemykh sistemakh (Modeling Reflexive Strategies in Controllable Systems), Moscow: Vychisl. Tsentr Ross. Akad. Nauk, 2001.

    Google Scholar 

  2. Lavlinskii, S.M., Gosudarstvenno–chastnoe partnerstvo na syr’evoi territorii—ekologicheskie problemy, modeli i perspektivy (Public–Private Partnership on Raw Material Territories: Ecological Problems, Models, and Prospects), Probl. Prognozirovaniya, 2010, no. 1, pp. 99–111.

    Google Scholar 

  3. Kochetov, Yu.A., Lavlinskii, S.M., Panin, A.A., and Plyasunov, A.V., Computational Complexity of Planning Models for Public–Private Partnership, Proc. 12th Int. Asian School Seminar “Optimization Problems for Complex Systems,” 2016, pp. 290–297.

    Google Scholar 

  4. Lavlinskii, S.M., Panin, A.A., and Plyasunov, A.V., A Bilevel Planning Model for Public–Private Partnership, Autom. Remote Control, 2015, vol. 76, no. 11, pp. 1976–1987.

    Article  MathSciNet  MATH  Google Scholar 

  5. Lavlinskii, S.M., Panin, A.A., and Plyasunov, A.V., Comparison of Models of Planning the Public–Private Partnership, J. Appl. Ind. Math., 2016, vol. 10, no. 3, pp. 356–369.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ausiello, G., Crescenzi, P., Gambosi, G., et al., Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Berlin: Springer–Verlag, 1999.

    Book  MATH  Google Scholar 

  7. Panin, A.A., Pashchenko, M.G., and Plyasunov, A.V., Bilevel Competitive Facility Location and Pricing Problems, Autom. Remote Control, 2014, vol. 75, no. 4, pp. 715–727.

    Article  MathSciNet  MATH  Google Scholar 

  8. Panin, A.A. and Plyasunov, A.V., On Complexity of Bilevel Problems of Location and Pricing, J. Appl. Ind. Math., 2014, vol. 8, no. 4, pp. 574–581.

    Article  MathSciNet  MATH  Google Scholar 

  9. Eggermont, C.E.J. and Woeginger, G.J., Motion Planning with Pulley, Rope, and Baskets, Theory Comput. Syst., 2013, vol. 53, no. 4, pp. 569–582.

    Article  MathSciNet  MATH  Google Scholar 

  10. Ben–Ayed, O., Bilevel Linear Programming, Comput. Oper. Res., 1993, vol. 20, no. 5, pp. 485–501.

    Article  MathSciNet  MATH  Google Scholar 

  11. Ivanov, S.V., Bilevel Stochastic Linear Programming Problems with Quantile Criterion, Autom. Remote Control, 2014, vol. 75, no. 1, pp. 107–118.

    Article  MathSciNet  MATH  Google Scholar 

  12. Ivanov, S.V. and Morozova, M.V., Stochastic Problem of Competitive Location of Facilities with Quantile Criterion, Autom. Remote Control, 2016, vol. 77, no. 3, pp. 451–461.

    Google Scholar 

  13. Kibzun, A.I. and Kan, Yu.S., Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami (Stochastic Programming Problems with Probabilistic Criteria), Moscow: Fizmatlit, 2009.

    MATH  Google Scholar 

  14. Alekseeva, E., Kochetov, Y., and Talbi, El–G., A Metaheuristic for the Discrete Bilevel Problem with Multiple Objectives at the Lower Level, Int. Trans. Oper. Res., 2017, vol. 24, no. 5, pp. 959–981.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to S. M. Lavlinskii, A. A. Panin or A. V. Plyasunov.

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Russian Text © S.M. Lavlinskii, A.A. Panin, A.V. Plyasunov, 2019, published in Avtomatika i Telemekhanika, 2019, No. 2, pp. 111–124.

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Lavlinskii, S.M., Panin, A.A. & Plyasunov, A.V. The Stackelberg Model in Territorial Planning. Autom Remote Control 80, 286–296 (2019). https://doi.org/10.1134/S0005117919020073

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  • DOI: https://doi.org/10.1134/S0005117919020073

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