Nonlinear integer transportation problem with additional supply and consumption points
An iterative decomposition method based on the sequential solution of two-dimensional problems subject to constraints from different groups is successfully applied to the case of integer transportation problems with convex objective functions and ascribed suppliers and consumers is proposed. Through...
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| Published in: | Journal of computer & systems sciences international Vol. 54; no. 1; pp. 86 - 92 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Moscow
Pleiades Publishing
2015
Springer Nature B.V |
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| Abstract | An iterative decomposition method based on the sequential solution of two-dimensional problems subject to constraints from different groups is successfully applied to the case of integer transportation problems with convex objective functions and ascribed suppliers and consumers is proposed. Through the introduction of new variables, it has been possible to extend the constructions of the algorithm in which the central point is the solution of optimization problems with two constraints. A detailed analysis of these problems is presented in the present paper. |
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| AbstractList | An iterative decomposition method based on the sequential solution of two-dimensional problems subject to constraints from different groups is successfully applied to the case of integer transportation problems with convex objective functions and ascribed suppliers and consumers is proposed. Through the introduction of new variables, it has been possible to extend the constructions of the algorithm in which the central point is the solution of optimization problems with two constraints. A detailed analysis of these problems is presented in the present paper. |
| Author | Leonov, V. Yu Esenkov, A. S. Tsurkov, V. I. Tizik, A. P. |
| Author_xml | – sequence: 1 givenname: A. S. surname: Esenkov fullname: Esenkov, A. S. organization: Dorodnicyn Computing Center, Russian Academy of Sciences – sequence: 2 givenname: V. Yu surname: Leonov fullname: Leonov, V. Yu organization: Dorodnicyn Computing Center, Russian Academy of Sciences – sequence: 3 givenname: A. P. surname: Tizik fullname: Tizik, A. P. email: Tizik_ap@mail.ru organization: Dorodnicyn Computing Center, Russian Academy of Sciences – sequence: 4 givenname: V. I. surname: Tsurkov fullname: Tsurkov, V. I. organization: Dorodnicyn Computing Center, Russian Academy of Sciences |
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| DOI | 10.1134/S1064230715010050 |
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| Keywords | Coupling Variable Transportation Problem System Science International Transportation Type Dimensional Problem |
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| References | Mironov, Tsurkov (CR18) 1995; 35 Mironov, Tsurkov (CR10) 2003; 42 Mironov, Fedorchuk, Tsurkov (CR11) 2005; 44 Tizik, Tsurkov (CR17) 1990; 28 Mironov, Levkina, Tsurkov (CR6) 2009; 8 Gol’shtein, Yudin (CR2) 1969 Mironov, Tsurkov (CR16) 1994; 32 Tizik, Tsurkov (CR1) 2012; 73 Sokolov, Tizik, Tsurkov (CR5) 2013; 52 Trius (CR3) 1967 Mironov, Tsurkov (CR14) 2001; 64 Mironov, Tsurkov (CR20) 1995 Mironov, Tsurkov (CR9) 1998; 37 Tsurkov (CR22) 1980; 250 Mironov, Tsurkov (CR7) 1994; 336 Esenkov, Kuzovlev, Leonov, Tizik, Tsurkov (CR4) 2014; 53 Mironov, Tsurkov (CR15) 1995; 33 Mironov, Tsurkov (CR12) 2002; 63 Mironov, Tsurkov (CR19) 1998; 37 Tizik, Tsurkov (CR21) 2012 Mironov, Tsurkov (CR13) 2001; 64 Mironov, Tsurkov (CR8) 1996; 346 A A Sokolov (6502_CR5) 2013; 52 A A Mironov (6502_CR13) 2001; 64 E B Trius (6502_CR3) 1967 A A Mironov (6502_CR14) 2001; 64 A A Mironov (6502_CR7) 1994; 336 A A Mironov (6502_CR8) 1996; 346 A A Mironov (6502_CR19) 1998; 37 E G Gol’shtein (6502_CR2) 1969 A A Mironov (6502_CR11) 2005; 44 A A Mironov (6502_CR15) 1995; 33 A A Mironov (6502_CR6) 2009; 8 A A Mironov (6502_CR9) 1998; 37 A A Mironov (6502_CR12) 2002; 63 V I Tsurkov (6502_CR22) 1980; 250 A A Mironov (6502_CR10) 2003; 42 A A Mironov (6502_CR16) 1994; 32 A A Mironov (6502_CR18) 1995; 35 A S Esenkov (6502_CR4) 2014; 53 A A Mironov (6502_CR20) 1995 A P Tizik (6502_CR21) 2012 A P Tizik (6502_CR1) 2012; 73 A P Tizik (6502_CR17) 1990; 28 |
| References_xml | – volume: 64 start-page: 374 year: 2001 end-page: 377 ident: CR13 article-title: Open transportation models with minimax criterion publication-title: Dokl. Math. contributor: fullname: Tsurkov – volume: 63 start-page: 388 year: 2002 end-page: 398 ident: CR12 article-title: Closed transportation models with minimax criterion publication-title: Autom. Remote Control doi: 10.1023/A:1014794115686 contributor: fullname: Tsurkov – volume: 37 start-page: 97 year: 1998 end-page: 944 ident: CR19 article-title: Hereditarily minimax matrices in models of transportation type publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: Tsurkov – start-page: 109 year: 1995 end-page: 118 ident: CR20 article-title: Transport-type problems with a criterion publication-title: Avtom. Telemekh., No. 12 contributor: fullname: Tsurkov – volume: 250 start-page: 304 issue: 2 year: 1980 end-page: 307 ident: CR22 article-title: An Iterative Method of the Decomposition for Extremum Problems publication-title: Doklady akademii nauk contributor: fullname: Tsurkov – volume: 73 start-page: 134 year: 2012 end-page: 143 ident: CR1 article-title: Iterative functional modification method for solving a transportation problem publication-title: Autom. Remote Control doi: 10.1134/S0005117912010109 contributor: fullname: Tsurkov – volume: 53 start-page: 369 year: 2014 end-page: 383 ident: CR4 article-title: Network optimization and problems with coupling variables publication-title: J. Comput. Syst. Sci. Int. doi: 10.1134/S1064230714030071 contributor: fullname: Tsurkov – volume: 64 start-page: 351 year: 2001 end-page: 354 ident: CR14 article-title: Minimax under nonlinear transportation constraints publication-title: Dokl. Math. contributor: fullname: Tsurkov – volume: 28 start-page: 24 issue: 2 year: 1990 end-page: 31 ident: CR17 article-title: Optimal channel distribution in communications networks publication-title: Sov. J. Comput. Syst. Sci. contributor: fullname: Tsurkov – volume: 8 start-page: 216 year: 2009 end-page: 226 ident: CR6 article-title: Minimax estimations of arc weights in integer networks with fixed node degrees publication-title: Appl. Comput. Math. contributor: fullname: Tsurkov – volume: 33 start-page: 107 issue: 3 year: 1995 end-page: 116 ident: CR15 article-title: Network models with fixed parameters at the communication nodes. 1 publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: Tsurkov – year: 1969 ident: CR2 publication-title: Linear Programming Problems of Transportation Type contributor: fullname: Yudin – volume: 52 start-page: 588 year: 2013 end-page: 598 ident: CR5 article-title: Iterative method for the transportation problem with additional supply and consumption points and quadratic cost publication-title: J. Comput. Syst. Sci. Int. doi: 10.1134/S106423071304014X contributor: fullname: Tsurkov – start-page: 148 year: 2012 end-page: 158 ident: CR21 article-title: Metod posledovatel’noi modifikatsii funktsionala dlya resheniya transportnoi zadachi publication-title: Avtom. Telemekh., No. 1 contributor: fullname: Tsurkov – volume: 346 start-page: 168 year: 1996 end-page: 171 ident: CR8 article-title: Transport Problems with a Minimax Criterion publication-title: Dokl. Ross. Akad. Nauk contributor: fullname: Tsurkov – volume: 42 start-page: 562 year: 2003 end-page: 574 ident: CR10 article-title: Minimax transportation models with integral constraints. I publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: Tsurkov – volume: 32 start-page: 1 issue: 6 year: 1994 end-page: 11 ident: CR16 article-title: Network models with fixed parameters at the communication nodes. 2 publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: Tsurkov – volume: 35 start-page: 15 year: 1995 end-page: 30 ident: CR18 article-title: Transport and network problems with the minimax criterion publication-title: Comput. Math. Math. Phys. contributor: fullname: Tsurkov – volume: 44 start-page: 732 year: 2005 end-page: 752 ident: CR11 article-title: Minimax transportation models with integral constraints. II publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: Tsurkov – year: 1967 ident: CR3 publication-title: Mathematical Programming Problems of Transportation Type contributor: fullname: Trius – volume: 336 start-page: 35 year: 1994 end-page: 38 ident: CR7 article-title: Class of distribution problems with minimax criterion publication-title: Dokl. Ross. Akad. Nauk contributor: fullname: Tsurkov – volume: 37 start-page: 927 year: 1998 end-page: 944 ident: CR9 article-title: Hereditarily minimax matrices in models of transportation type publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: Tsurkov – volume: 37 start-page: 927 year: 1998 ident: 6502_CR9 publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: A A Mironov – volume: 42 start-page: 562 year: 2003 ident: 6502_CR10 publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: A A Mironov – volume: 73 start-page: 134 year: 2012 ident: 6502_CR1 publication-title: Autom. Remote Control doi: 10.1134/S0005117912010109 contributor: fullname: A P Tizik – volume-title: Mathematical Programming Problems of Transportation Type year: 1967 ident: 6502_CR3 contributor: fullname: E B Trius – volume: 33 start-page: 107 issue: 3 year: 1995 ident: 6502_CR15 publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: A A Mironov – volume: 37 start-page: 97 year: 1998 ident: 6502_CR19 publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: A A Mironov – volume: 28 start-page: 24 issue: 2 year: 1990 ident: 6502_CR17 publication-title: Sov. J. Comput. Syst. Sci. contributor: fullname: A P Tizik – start-page: 148 volume-title: Avtom. Telemekh., No. 1 year: 2012 ident: 6502_CR21 contributor: fullname: A P Tizik – volume: 32 start-page: 1 issue: 6 year: 1994 ident: 6502_CR16 publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: A A Mironov – volume: 336 start-page: 35 year: 1994 ident: 6502_CR7 publication-title: Dokl. Ross. Akad. Nauk contributor: fullname: A A Mironov – volume: 346 start-page: 168 year: 1996 ident: 6502_CR8 publication-title: Dokl. Ross. Akad. Nauk contributor: fullname: A A Mironov – volume: 35 start-page: 15 year: 1995 ident: 6502_CR18 publication-title: Comput. Math. Math. Phys. contributor: fullname: A A Mironov – volume: 250 start-page: 304 issue: 2 year: 1980 ident: 6502_CR22 publication-title: Doklady akademii nauk contributor: fullname: V I Tsurkov – volume: 63 start-page: 388 year: 2002 ident: 6502_CR12 publication-title: Autom. Remote Control doi: 10.1023/A:1014794115686 contributor: fullname: A A Mironov – volume: 52 start-page: 588 year: 2013 ident: 6502_CR5 publication-title: J. Comput. Syst. Sci. Int. doi: 10.1134/S106423071304014X contributor: fullname: A A Sokolov – volume-title: Linear Programming Problems of Transportation Type year: 1969 ident: 6502_CR2 contributor: fullname: E G Gol’shtein – volume: 64 start-page: 374 year: 2001 ident: 6502_CR13 publication-title: Dokl. Math. contributor: fullname: A A Mironov – start-page: 109 volume-title: Avtom. Telemekh., No. 12 year: 1995 ident: 6502_CR20 contributor: fullname: A A Mironov – volume: 53 start-page: 369 year: 2014 ident: 6502_CR4 publication-title: J. Comput. Syst. Sci. Int. doi: 10.1134/S1064230714030071 contributor: fullname: A S Esenkov – volume: 44 start-page: 732 year: 2005 ident: 6502_CR11 publication-title: J. Comput. Syst. Sci. Int. contributor: fullname: A A Mironov – volume: 8 start-page: 216 year: 2009 ident: 6502_CR6 publication-title: Appl. Comput. Math. contributor: fullname: A A Mironov – volume: 64 start-page: 351 year: 2001 ident: 6502_CR14 publication-title: Dokl. Math. contributor: fullname: A A Mironov |
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| SubjectTerms | Algorithms Computer science Consumers Consumption Control Engineering Integers Mathematical analysis Mathematical models Mechatronics Nonlinear programming Numbers Optimization Optimization algorithms Robotics Studies Suppliers Systems Analysis and Operations Research Transportation problem Transportation problem (Operations research) Variables |
| Title | Nonlinear integer transportation problem with additional supply and consumption points |
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