Abstract
Mathematical methods of optimization for strategic planning and operations management in transportation systems considered in the present book provide solutions for basic problems in the field detected and formulated in [1] as optimization problems. The list of such problems is presented in the table contained in the Introduction. These problems encompass a variety of practical situations beginning with those for various types of transport and finishing with problems of analyzing transport as a part of an infrastructure of the national economy complex [2]. These methods form the main mathematical tools used today in the research and practical strategic planning and operations management in transportation systems. However, the process of increasing the activity in mathematical modeling in transportation systems and in that of detecting new problems that may be formalized and researched on the basic of mathematical models is extremely intensive. In the course of this process, new optimization methods within the framework of known classes of problems, as well as new formulations of problems necessitating the use of different existing mathematical tools or working out the new ones appear [3]. In the author’s opinion, two directions of researching transportation systems will shortly acquire a practical turn and demand using and working out new mathematical tools. These directions for which outlines of the tools are becoming more and more evident in the process of the directions development are briefly discussed below.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Belen’kii, A. S. Matematicheskie Modeli Optimal’nogo Planirovanija v Transportnykh Sistemakh. Itogi nauki i tekhniki. Seria Organizatzija Upravlenija Transportom (Mathematical Models of Optimal Planning in Transportation Systems. Frontiers of Science and Technology. Series Organization of Transportation Management). Moscow: VINITI, 7, 1988 [in Russian].
Belen’kii, A. S. Metody Optimal’nogo Planirovanija na Transporte (Optimum Planning Methods for Transport). Moscow: Znanie, 1988 [in Russian]
Belen’kii, A. S. Prikladnaja Matematika v Narodnom Khozjaistve (Applied Mathematics in National Economy). Moscow Znanie, 1985 [in Russian].
Tzvirkun, A. D., Akinfiev, V. K., and Solov’ev, M. M. Modelirovanie Razvitija Krupnomasschtabnykh Sistem (Modeling of Developing Large-Scale Systems). Moscow: Ekonomika, 1983 [in Russian].
Livshitz, V. N. Sistemnyj Analiz Ekonomicheskikh Processov na Transporte (System Analysis of Economic Processes for Transport). Moscow: Transport, 1986 [in Russian].
Dyukalov, A. N., and Ilyutovich, A. E. Asymptotic properties of optimal trajectories in economic dynamics. Automation and Remote Control. 1973; 34, No. 3: 423–434.
Tzvirkun, A. D., Karibskii, A. V., and Yakovenko, S. Yu. Matematicheskoe Modelirovanie Upravlenija Razvitiem Struktur Krupnomasschtabnykh Sistem. Preprint (Mathematical Modeling of Control of Developing Large-Scale Systems. Preprint). Moscow: Izd. Institut Problem Upravleniya ( Institute of Control Sciences, USSR Academy of Sciences ), 1985 [in Russian].
Rubinov, A. M. Ekonomicheskaja Dinarnika. Sovremennye Problemy (Economic Dynamics. Contemporary Problems of Mathematics). Moscow: VINITI, 1982, 19 [in Russian].
Cheremnykh, Yu. N. Matematicheskoe Modelirovanie Narodnokhozjaistvennoi Dinamiki (Mathematical Modeling of Dynamics of National Economy). Moscow: Nauka, 1982 [in Russian].
Cheremnykh, Yu. N. Analiz Povedenija 7’raektorii Dinamiki Narodnokhozjaistvennykh Modelei (Behavioral Analysis of Trajectories of National Economy Models Dynamics). Moscow: Nauka, 1982 [in Russian].
Teplova, T. V. “Turnpike approach in dynamic multi-sector models with nonlinear dependences.” In Matematicheskie Metody Analiza Ekonomiki (Mathematical Methods of Economy Analysis). Moscow: Izd. MGU (Moscow State University), 1987; 188–199 [in Russian].
Hori, H. A turnpike theorem for rolling plans. Journal of Mathematical Economics. 1987; 16, No. 3: 223–235.
Zaslaysky, A. Ya. “Turnpike sets in models of economic dynamics.” In Optimizatzija (Optimization). Novosibirsk: Institute of Mathematics, Novosibirsk: 1988; No. 3: 427–441 [in Russian].
Borisov, K. Yu. “Turnpike features of optimal trajectories in models of economic dynamics.” In Optimizatzija (Optimization). Novosibirsk: Institute of Mathematics, Siberian Division of the USSR Academy of Sciences, 1987; 41 (58), 76–87 [in Russian].
Marcotte, P. A new algorithm for solving variational inequalities with application to the traffic assignment problem. Mathematical Programming. 1985; 33, No. 3: 339–351.
Smith, M. J. The existence of a time-dependent equilibrium distribution of arrivals at a single bottleneck. Transportation Science. 1984; 18, No. 4: 385–394.
Iwantschew, D. Optimierungsprobleme zur Vitalitat von Netzwerken. Int. Tag.: Math. Optimierungstheor. and Anwend. Eisenach, 10–15 Nov.. Vortragsanzuge. Ilmenau, s.a., 1986; 180–181.
Kanemoto, Y., and Mera, K. General equilibrium analysis of the benefits of large transportation improvements. Discussion Paper. Institute of Economics Research. Queen’s University. 1984; No. 567.
Granja, L., and Mora-Catino, F. Modeles entropiques multimodaux de prevision de flux de transport. RAIRO Recherche Operationnelle/Operations Research. 1985; 19, No. 2: 143–158.
Scott, C. H., McMillan, H., and Jefferson, T. R. Equilibria and convex cost networks. International Journal of Systems Science. 1986; 17, No. 7: 1007–1013.
Maugeri, A. Convex programming, variational inequalities, and applications to the traffic equilibrium problem. Applied Mathematics and Optimization. 1987; 16, No. 2: 169–185.
Fukushima, M., and Itoh, T. A dual approach to asymmetric traffic equilibrium problems. Mathematica Japonica. 1987; 32, No. 5: 701–721.
Itoh, T., Fukushima, M., and Ibaraki, T. An iterative method for variational inequalities with application to traffic equilibrium problems. Journal of the Operations Research Society of Japan. 1988; 31, No. 1: 82–103.
Maugeri, A. Stability results for variational inequalities and applications to traffic equilibrium problem. Rendiconti. Circolo Mathematico di Palermo. 1986; 34, Suppl. No. 8: 269–280.
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Belenky, A.S. (1998). Conclusion. In: Operations Research in Transportation Systems. Applied Optimization, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6075-0_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6075-0_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4803-8
Online ISBN: 978-1-4757-6075-0
eBook Packages: Springer Book Archive