Application of n-distance balanced graphs in distributing management and finding optimal logistical hubs

Document Type : Research Paper


1 School of Mathematics , Iran University of Science and Technology, Tehran , Iran

2 School of Mathematics‎, ‎Iran University of Science and Technology, Narmak‎, ‎Tehran‎, ‎Iran


Optimization and reduction of costs in management of distribution and transportation of commodity are one of the main goals of many organizations. Using suitable models in supply chain in order to increase efficiency and appropriate location for support centers in logistical networks is highly important for planners and managers. Graph modeling can be used to analyze these problems and many others such as the management of municipal services and traffic control. To achieve these goals, we suggest some models based on structure of distance balanced graphs, and 15n"> -distance balanced graphs. These graphs can be considered as a model in communication networks in order to avoid additional costs and maintain balance in networks.


Main Subjects

Alaeiyan, M., & Kharazi, H., (2016). Optimal network protection against interdiction strategies via evolutionary algorithms. Malaya Journal of Matematik, In Press.
Balakrishnan, K., Brešar, B., Changat, M., Klavžar, S., Vesel, A., & Pleteršek, P. Ž. (2014). Equal opportunity networks, distance-balanced graphs, and Wiener game. Discrete Optimization, 12, 150-154.
Brandes, U., & Erlebach, T. (2005). Network analysis: methodological foundations (Vol. 3418). Springer Science & Business Media.
Chang, P. Y., & Lin, H. Y. (2015). Manufacturing plant location selection in logistics network using Analytic Hierarchy Process. Journal of Industrial Engineering and Management, 8(5), 1547-1575.
Creaco, E., Alvisi, S., & Franchini, M. (2014). A multi-step approach for optimal design and management of the C-Town pipe network model. Procedia Engineering, 89, 37-44.
Dave, D., & Jhala, N. (2014). Application of graph theory in traffic management. International Journal of Engineering and Innovative Technology, 3(12), 124-126.
Dixon, I., & Lundeen, A. (2004). Cost-effectiveness analysis: An employer decision support tool. National Business Group on Health.
Harary, F. (2013). Graph theoretic methods in the management. Social Networks: A Developing Paradigm, 371.
Jerebic, J., Klavžar, S., & Rall, D. F. (2008). Distance-balanced graphs. Annals of Combinatorics, 12(1), 71-79.
Likaj, R., Shala, A., Mehmetaj, M., Hyseni, P., & Bajrami, X., (2013). Application of graph theory to find optimal paths for the transportation problem. IFAC Proceedings Volumes, 46(8), 235-240.
Maity, S. K., Bhattacharyya, B. K., & Bhattacharyya, B. (2015). Implementation of graph theory in municipal solid waste management. International Journal of Environment and Waste Management, 16(3), 197-208.
Ruchansky, N., Bonchi, F., García-Soriano, D., Gullo, F., & Kourtellis, N. (2015, May). The minimum wiener connector problem. In Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data (pp. 1587-1602). ACM.
Tamura, H., Nakano, K., Sengoku, M., & Shinoda, S. (2011). On applications of graph/network theory to problems in communication systems. On Computer and Information Technology Volume, 5(1), 15-21.
Vanhook, P. M. (2007). Cost-utility analysis: A method of quantifying the value of registered nurses. Online Journal of Issues in Nursing, 12(3).
Wagner, S. M., & Neshat, N. (2010). Assessing the vulnerability of supply chains using graph theory. International Journal of Production Economics, 126(1), 121-129.
Zhong, H. (2014). Game analysis of product-service integration. Journal of Industrial Engineering and Management, 7(5), 1447-1467.