- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 612142, 12 pages
Traffic Network Equilibrium Problems with Capacity Constraints of Arcs and Linear Scalarization Methods
1Chongqing University of Science and Technology, Chongqing 401331, China
2College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Received 13 September 2012; Accepted 15 November 2012
Academic Editor: Nan-Jing Huang
Copyright © 2012 X. Q. Tian and Y. D. Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Wardrop, “Some theoretical aspects of road traffic research,” Proceedings of the Institute of Civil Engineers, vol. 1, pp. 325–378, 1952.
- Q. Meng, Y. K. Huang, and R. L. Cheu, “A note on supply chain network equilibrium models,” Transportation Research E, vol. 43, no. 1, pp. 60–71, 2007.
- A. Nagurney and J. Dong, “A multiclass, multicriteria traffic network equilibrium model with elastic demand,” Transportation Research B, vol. 36, no. 5, pp. 445–469, 2002.
- A. Nagurney, J. Dong, and D. Zhang, “A supply chain network equilibrium model,” Transportation Research E, vol. 38, no. 5, pp. 281–303, 2002.
- A. Nagurney, “On the relationship between supply chain and transportation network equilibria: a supernetwork equivalence with computations,” Transportation Research E, vol. 42, no. 4, pp. 293–316, 2006.
- G. Y. Chen and N. D. Yen, On the Variational Inequality Model For Network Equilibrium, vol. 724, Department of Mathematics, University of Pisa, 1993, Internal Report 3.
- P. Q. Khanh and L. M. Luu, “On the existence of solutions to vector quasivariational inequalities and quasicomplementarity problems with applications to traffic network equilibria,” Journal of Optimization Theory and Applications, vol. 123, no. 3, pp. 533–548, 2004.
- P. Q. Khanh and L. M. Luu, “Some existence results for vector quasivariational inequalities involving multifunctions and applications to traffic equilibrium problems,” Journal of Global Optimization, vol. 32, no. 4, pp. 551–568, 2005.
- G. Y. Chen, C. J. Goh, and X. Q. Yang, “Vector network equilibrium problems and nonlinear scalarization methods,” Mathematical Methods of Operations Research, vol. 49, no. 2, pp. 239–253, 1999.
- T. C. E. Cheng and Y. N. Wu, “A multiproduct, multicriterion supply-demand network equilibrium model,” Operations Research, vol. 54, no. 3, pp. 544–554, 2006.
- S. J. Li, X. Q. Yang, and G. Y. Chen, “A note on vector network equilibrium principles,” Mathematical Methods of Operations Research, vol. 64, no. 2, pp. 327–334, 2006.
- S. J. Li, K. L. Teo, and X. Q. Yang, “A remark on a standard and linear vector network equilibrium problem with capacity constraints,” European Journal of Operational Research, vol. 184, no. 1, pp. 13–23, 2008.
- S. J. Li, K. L. Teo, and X. Q. Yang, “Vector equilibrium problems with elastic demands and capacity constraints,” Journal of Global Optimization, vol. 37, no. 4, pp. 647–660, 2007.
- C. J. Goh and X. Q. Yang, “Vector equilibrium problem and vector optimization,” European Journal of Operational Research, vol. 116, no. 3, pp. 615–628, 1999.
- F. Raciti, “Equilibrium conditions and vector variational inequalities: a complex relation,” Journal of Global Optimization, vol. 40, no. 1–3, pp. 353–360, 2008.
- X. Q. Yang and C. J. Goh, “On vector variational inequalities: application to vector equilibria,” Journal of Optimization Theory and Applications, vol. 95, no. 2, pp. 431–443, 1997.
- D. T. Luc, M. Rocca, and M. Papalia, “Equilibrium in a vector supply-demand network with capacity constraints,” Applicable Analysis, vol. 90, no. 6, pp. 1029–1045, 2011.
- Z. Lin, “The study of traffic equilibrium problems with capacity constraints of arcs,” Nonlinear Analysis. Real World Applications, vol. 11, no. 4, pp. 2280–2284, 2010.
- Z. Lin, “On existence of vector equilibrium flows with capacity constraints of arcs,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 72, no. 3-4, pp. 2076–2079, 2010.
- Y. D. Xu, S. J. Li, and K. L. Teo, “Vector network equilibrium problems with capacity constraints of arcs,” Transportation Research E, vol. 48, pp. 567–577, 2012.
- A. Zaffaroni, “Degrees of efficiency and degrees of minimality,” SIAM Journal on Control and Optimization, vol. 42, no. 3, pp. 1071–1086, 2003.
- J. Jahn, Vector Optimization. Theory, Applications, and Extensions, Springer, Berlin, Germany, 2004.