Abstract
Foundations of theory of transportation problems were laid by Hitchcock [43]. Note, however, that some particular problems were examined earlier (see [39]). The scope of transportation models is very wide. We can mention problems related, for example, to design of production and shipments, to creation of computation and information systems, to allocation of resources and stocks, etc. [14, 27, 28, 42].
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 to Chapter 1
Alekseev V.M., Tikhomirov V.M., and Fomin S.V., Optimal’noe upravlenie (Optimal Control), Moscow: Nauka, 1979.
Astakhov N. D., Fedoseev A.V., and Chan Van Khung, O primenenii uskoren-nykh algoritmov resheniya zadach transportnogo tipa (On the Use of Accelerated Algorithms for Solving Transportation Problems), Moscow: Computing Center of Russ. Acad. Sei., 1994.
Bellman R. Dynamic Programming, Princeton: Princeton Univ. Press, 1957.
Burkov V.N, Matematicheskie osnovy teorii aktivnykh sistem (Mathematical Foundations of the Theory of Active Systems), Moscow: Nauka, 1977.
Burkov V.N. and Opoitsev V.N., Metagame Approach to Hierarchical Systems Control, Avtom. Telemekh., 1974, no. 1, pp. 103–114.
Teoretiko-igrovye voprosy prinyatiya reshenii (Game-Theoretic Problems in Decision Making), Vorob’eva, N.N., Ed., Leningrad: Nauka,1978.
Gale D, A Theorem on Flow in Networks, Pacific J. Math., 1957, vol. 7, pp. 1073–1082.
Gnedenko B.V., Kurs teorii veroyatnostei (A Course in Probability Theory), Moscow: Fizmatgiz, 1969.
Gol’shtein E.G. and Yudin D.B, Zadachi lineinogo programmirovania transportnogo tipa (Transportation Problems in Linear Programming), Moscow: Nauka, 1969.
Dem’yaninov V. F. and Malozemov V. N., Vvedenie v minimaks (Introduction to Minimax), Moscow: Nauka, 1972.
Emelichev V. A. and Kovalev M.M., Mnogogranniki, grafy, optimizatsiya (Polyhedrons, Graphs, and Optimization), Moscow: Nauka, 1981.
Emelichev V.A. and Kononenko A.M., On a Class of Transportation Polyhedrons, Izv. Belarus. Akad. Nauk., Ser. Fiz. Mat., 1971, no. 3, pp. 21–23.
Emelichev V.A., Kravtsov M.K., and Krachkovski A. P., On Some Classes of Transportation Polyhedrons, Dokl Akad. Nauk SSSR, 1978, vol. 241, no. 3, pp. 34–37.
Zolotov A. V., Kim K. V., Mgeryan G. M., and Khachaturov V. R., Algoritmicheskoe i programmnoe obespechenie resheniya zadach operativnogo planirovaniya transportnykh perevozok (Algorithms and Software for Short-Term Planning of Shipments), Moscow: Computing Center of Russ. Acad. Sei., 1989.
Ioffe A.D. and Tikhomirov V.M., Teoriya ekstremal’nykh zadach (Theory of Extremum Value Problems), Moscow: Nauka, 1974.
Karmanov V.G., Matematicheskoe programmirovanie (Mathematical programming), Moscow: Nauka, 1986.
Kononenko A.M. and Trukhanovskii N.N., On Transport Polyhedrons with Maximal Number of Vertices, Izv. Belarus. Akad. Nauk, Ser. Fiz. Mat., 1978, no. 5, pp. 23–25.
Krasnoshchekov P. S. and Petrov A. A., Printsipy postroeniya modelet (Principles of Model Construction), Moscow: Mosk. Gos. Univ., 1983.
Kuznetsov A. V., Sakovich V. A., and Kholod N.N., Vysshaya matematika. Matematicheskoe programmirovanie (Higher Mathematics: Mathematical programming), Minsk: Vysshaya Shkola, 1994.
Kuhn H.V. and Tucker A.W., Nonlinear Programming, Proc. of the Second Berkeley Symp. on Math. Statistics and Probability, Berkeley: Univ. of California Press, 1951, pp. 481–492.
Marcus M. and Mink H., Matrix Theory and Matrix Inequalities, Boston: Allyn and Bacon, 1964. Translated under the title Obzor po teorii matrits i matrichnykh neravenstv, Moscow: Nauka, 1972.
Mironov A. A. and Tsurkov V. I., A Class of Distributed Problems with Minimax Criteria, Dokl. Akad. Nauk, 1992, vol. 336, no. 1, pp. 35–38.
Mironov A.A. and Tsurkov V.I., Transportation and Network Problems with Minimax Criteria, Zh. Vychisl. Mat. Mat. Fiz., 1995, vol. 35, no. 1, pp. 24–45.
Mironov A.A. and Tsurkov V.I., Transportation Problems with Minimax Criteria, Avtom. Telemekh., 1995, no. 12, pp. 109–118.
Mironov A.A. and Tsurkov V.I., Transportation Problems with Minimax Criteria, Dokl. Akad. Nauk, 1996, vol. 346, no. 2, pp. 1–4.
Sovremennoe sostoyanie teorii issledovaniya operatsii (Modern Theory of Operations Research), Moiseev, N.N., Ed., Moscow: Nauka, 1979.
Moder J. and Elmaghraby S.S., Handbook of Operations Research, New York: Van Nostrand, 1978. Translated under the title Issledovanie operatsii. Metodologicheskie osnovy i matematicheskie metody, vol. 1, Moscow: Mir, 1981.
Moder J. and Elmaghraby S.S., Handbook of Operations Research, New York: Van Nostrand, 1978. Translated under the title Issledovanie operatsii. Modeli i primeneniya, vol. 2, Moscow: Mir, 1981.
Mukhacheva E.A. and Rubinshtein G.Sh., Matematicheskoe programmirovanie (Mathematical Programming), Novosibirsk: Nauka, 1977.
Neyman J. and Morgenshtein O., Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1953. Translated under the title Teoriya igr i economicheskoe povedenie, Moscow: Nauka, 1970.
Owen G., Game Theory, Philadelphia: Saunders, 1968. Translated under the title Teoriya igr, Moscow: Mir, 1971.
Panos M. Pardalos, Minimax and Applications, University of Minnesota and Institute of Applied Mathematics, Beijing: Academia Sinica, 1995.
Pshenichnyi B. N., Vypuklyi analiz i ekstremal’nye zadachi (Convex Analysis and Extremum Value Problems), Moscow: Nauka, 1980.
Riordan J., An Introduction to Combinatorial Analysis, New York: Wiley, 1958. Translated under the title Vvedenie v kombinatornyi analiz, Moscow: Inostr. Literatura, 1963.
Rockafellar R. T., Convex Analysis, Princeton: Princeton Univ. Press, 1970. Translated under the title Vypuklyi analiz, Moscow: Mir, 1973.
Saaty T., Optimization in Integers and Related Extremal Problems, New York: McGraw-Hill, 1970. Translated under the title Tselochislennye metody optimizat-sii i svyazannye s nimi ekstremal’nye problemy, Moscow: Mir, 1973.
Sachkov V.N., Vvedenie v kombinatornye metody diskretnoi matematiki (Introduction to Combinatorial Methods of Discrete Mathematics), Moscow: Nauka, 1982.
Sukharev A.G., Timokhov A. V., and Fedorov V. V., Kurs metodov optimizatsii (Lectures on Optimization Methods), Moscow: Nauka, 1986.
Tolstoi A.N., Elimination of Inefficient Shipments in Planning, Sotsialisticheskii Transport, 1939, no. 9, pp. 28–51.
Trius E.B., Zadachi matematicheskogo programmirovaniya transportnogo tipa (Transportation Problems in Mathematical Programming), Moscow: Sovetskoe Radio, 1967.
Ford L.R. and Fulkerson D., Flows in Networks, Princeton: Princeton Univ. Press, 1962. Translated under the title Potoki v setyakh, Moscow: Mir, 1966.
Khachaturov V.R. and Montlevich V.M., Reshenie nelineinykh proizvodstvenno-transportnykh zadach s nedelimymi potrebitelyami (Solution of Nonlinear Production Transportation Problems with Indivisible Consumers), Moscow: Computing Center of Russ. Acad. Sei., 1987.
Hitchcock F.L., Distribution of a Product from Several Sources to Numerous Localities, J. Math. Phys., 1941, vol. 20, pp. 224–230.
Hu T., Integer Programming and Network Flows, Reading (USA): Addison- Wesley, 1969. Translated under the title Tselochislennoe programmirovanie i potoki v setyakh, Moscow: Mir, 1974.
Tsurkov V.I., Dekompozitsiya v zadachakh bol’shoi razmernosti (Decomposition in Large-Scale Problems), Moscow: Nauka, 1981.
Tsurkov V. I., Dinamicheskie zadachi bol’shoi razmernosti (Dynamic Large-Scale Problems), Moscow: Nauka, 1988.
Tsurkov V. I. and Litvinichev I. S., Optimizatsiya i issledovanie operatsii. Dekompozitsiya v dinamicheskikh zadachakh s perekrestnymi svyazyami (Optimization and Operations Research: Decomposition in Dynamic Problems with Crossed Links), vol. 1, Moscow: Nauka, 1994.
Tsurkov V. I. and Litvinichev I. S., Optimizatsiya i issledovanie operatsii. Dekompozitsiya v dinamicheskikh zadachakh s perekrestnymi svyazyami (Optimization and Operations Research: Decomposition in Dynamic Problems with Crossed Links), vol. 2, Moscow: Nauka, 1994.
Chernikov S.N., Lineinye neravenstva (Linear Inequalities), Moscow: Nauka, 1968.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Tsurkov, V., Mironov, A. (1999). Transportation Models with Minimax Criteria and Preliminary Constructions. In: Minimax Under Transportation Constrains. Applied Optimization, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4060-1_1
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4060-1_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6818-2
Online ISBN: 978-1-4615-4060-1
eBook Packages: Springer Book Archive