• Alexander S. Belenky
Part of the Applied Optimization book series (APOP, volume 20)


The active, rapid penetration of computers into all the spheres of strategic planning and operations management has led to the intensive development of a number of scientific and engineering directions in the applied theory of control. Mathematical modeling and a part of operations research that is based on the theory and methods of optimization should be considered as the most important ones. Mathematical models for the description of various objects, along with the accumulated experience in using mathematical methods that enable one to solve problems formulated on the basis of the models, have grounded the tools for analysis and decision making in economic and technical systems. The tools include, in particular, mathematical models and methods for strategic planning and operations management implemented in various decision-making systems, which are widely used in almost all branches of the advanced economy, transportation being one of those. However, the degree of employing the tools in transportation still remains much lower than that in the other branches.


Schedule Problem Programming Problem Optimal Control Problem Strategic Planning Transportation System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Belen’kii, A. S. Matematicheskie Modeli Optimal’nogo Planirovanija v Transportnykh Sistemakh (Mathematical Models of Optimum Planning in Transportation Systems. Frontiers of Science and Technology. Series Organization of Transport Management). Moscow: VINITI, 7, 1988 [in Russian].Google Scholar
  2. [2]
    Belen’kii, A. S., and Levner, E. V. Scheduling models and methods in optimal freight transportation planning. Automation and Remote Control. 1989; 50, No. 1: 1–56.MathSciNetGoogle Scholar
  3. [3]
    Belen’kii, A. S. Search for min-max of two monotone functions in polyhedral set. Automation and Remote Control. 1982; 43, No. 11: 1389–1393.Google Scholar
  4. [4]
    Belen’kii, A. S. Soverschenstvovanie Planirovanija v Transportnykh Sistemakh (Metodologija i Opyt Primenenija Ekonomiko-Matematicheskikh Modelei i Metodov Optimal’nogo Planirovanija) (Perfecting Planning in Transportation Systems (Methodology and Practice of Applying Economics-Mathematic Models and Methods of Optimal Planning)). Moscow: Znanie, 1988 [in Russian].Google Scholar
  5. [5]
    Vasil’ev, F. P. Chislennye Metody Reschenia Ekstremal’nykh Zadach (Numerical Methods of Extreme Problems Solution). Moscow: Nauka, 1980 [in Russian].Google Scholar
  6. [6]
    Sovremennoe Sostojanie Teorii Issledovanija Operatzii. Redaktor N. N. Moiseev (State-of-the-art of Operations Research). Editor Moiseev, N. N. Moscow: Nauka, 1979 [in Russian].Google Scholar
  7. [7]
    Belen’kii, A. S. Prikladnaja Matematika v Narodnom Khozjaistve (Applied Mathematics in National Economy). Moscow: Znanie, 1985 [in Russian].Google Scholar
  8. [8]
    Boltianskiy, V. G. Mathematical Methods of Optimum Control. New York: Holt, Reinart and Winston, 1971.Google Scholar
  9. [9]
    Golshtein, E. G., and Yudin, D. B. Transportnaja Zadacha Lineinogo Programmirovanija (The Transportation Problem). Moscow: Nauka, 1979 [in Russian].Google Scholar
  10. [10]
    Polyak, B. T. Introduction to Optimization. New York: Optimization Software, Publications Division, 1987.Google Scholar
  11. [11]
    Pshenichnyi, B. N. Vypuklyi Analiz i Ekstremal’nye Zadachi (Convex Analysis and Extreme Problems). Moscow: Nauka, 1980 [in Russian].Google Scholar
  12. [12]
    Shor, N. Z. Minimization Methods for Non-Differentiable Functions. Berlin; New York: Springer—Verlag, 1985.Google Scholar
  13. [13]
    Yudin, D. B., and Yudin, A. D. Ekstremal’nye Modeli v Ekonomike (Extreme Models in Economics). Moscow: Ekonomika, 1979 [in Russian].Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Alexander S. Belenky

There are no affiliations available

Personalised recommendations