Geodesic
Minimum Cost Multicommodity Flows in Dynamic Networks and Algorithms for their Finding
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 107-119.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the minimum cost multicommodity flow problem in dynamic networks with time-varying capacities of arcs and transit times on arcs that depend on the sort of commodity entering them. We assume that cost functions, defined on arcs, are nonlinear and depend on time and flow, and the demand function also depends on time. Moreover, we study the problem in the case when transit time functions depend on time and flow. The modification of the time-expanded network method and new algorithms for solving the considered classes of problems are proposed. 
@article{BASM_2007_1_a10,
     author = {Maria Fonoberova and Dmitrii Lozovanu},
     title = {Minimum {Cost} {Multicommodity} {Flows} in {Dynamic} {Networks} and {Algorithms} for their {Finding}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {107--119},
     publisher = {mathdoc},
     number = {1},
     year = {2007},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2007_1_a10/}
}
TY  - JOUR
AU  - Maria Fonoberova
AU  - Dmitrii Lozovanu
TI  - Minimum Cost Multicommodity Flows in Dynamic Networks and Algorithms for their Finding
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2007
SP  - 107
EP  - 119
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2007_1_a10/
LA  - en
ID  - BASM_2007_1_a10
ER  - 
%0 Journal Article
%A Maria Fonoberova
%A Dmitrii Lozovanu
%T Minimum Cost Multicommodity Flows in Dynamic Networks and Algorithms for their Finding
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2007
%P 107-119
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2007_1_a10/
%G en
%F BASM_2007_1_a10
Maria Fonoberova; Dmitrii Lozovanu. Minimum Cost Multicommodity Flows in Dynamic Networks and Algorithms for their Finding. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 107-119. https://geodesic-test.mathdoc.fr/item/BASM_2007_1_a10/

[1] Fleisher L., Skutella M., “The quickest multicommodity flow problem”, Integer programming and combinatorial optimization, 2002, 36–53 | MR

[2] Fonoberova M., Lozovanu D., “Optimal multicommodity flows in dynamic networks and algorithms for their finding”, Bulletinul Academiei de Ştiinţe a Republicii Moldova, Matematica, 2005, no. 1(47), 19–34 | MR | Zbl

[3] Ford L., Fulkerson D., Flows in Networks, Princeton University Press, Princeton, NJ, 1962 | MR | Zbl

[4] Hoppe B., Tardos E., “The quickest transshipment problem”, Mathematics of Operations Research, 25 (2000), 36–62 | DOI | MR | Zbl

[5] Lozovanu D., Stratila D., “Optimal flow in dynamic networks with nonlinear cost functions on edges”, Analysis and optimization of differential systems, Kluwer Academic Publishers, 2003, 247–258 | MR | Zbl