Multi-modal and multi-product hierarchical hub location under uncertainty

Document Type : Research Paper


1 Master of Science in Industrial Engineering, Science and Technology University, Tehran, Iran

2 Prof., Dep. of Industrial Engineering, University of Science and Technology, Tehran, Iran

3 Assistant Prof. of Industrial Engineering, University of Science and Technology, Tehran, Iran


This paper aims to model and resolve single allocation multi-product hierarchical hub location problem with considering of uncertainty and quality of service. The designed hierarchical hub network has three levels that the top one consists of fully connected central hub nodes and second and third levels are star network of non-central hub nodes with central hub nodes and demand centers to hub nodes (central and non-central), respectively. In the proposed model, objective functions minimizes the sum of transportation and delay costs beside the cost of activating the inactive airline routs, and thereby optimal decision is made on location of hubs, allocation of non-hub nodes to hub nodes and the type of transportation vehicle. For evaluation of the proposed model a collected dataset of Iran is used. Sensitivity analysis of model’s behavior with parameters’ change is done and resulted in management implications.


Alumur, S. A., Yaman, H., & Kara, B. Y. (2012). Hierarchical multimodal hub location problem with time-definite deliveries. Transportation Research Part E: Logistics and Transportation Review, 48(6), 1107–1120.
Arshadi Khamseh, A. & Doost Mohamadi, M. (2014). Complete/Incomplete Hierarchical Hub Center Single Assignment Network Problem. Journal of Optimization in Industrial Engineering, 7(14), 1–12.
Baoding, L. (2004). Uncertainty theory: an introduction to its axiomatic foundations (1 edition), Springer.
Ben-Ayed, O. (2013). Parcel distribution network design problem. Operational Research, 13(2), 211–232.
Davari, S. & Fazel Zarandi, M. H. (2012). The single-allocation hierarchical hub median location problem with fuzzy demands. African Journal of Business Manegement, 6(1), 347–360.
Dubois, D., Prade, H., Farreny, H., Martin-Clouaire, R. & Testemale, C. (1988). Possibility Theory: An Approach to Computerized Processing of Uncertainty. New York: Collaboration of Plenum Press.
Ermoliev, Y. M., & Leonardi, G. (1982). Some proposals for stochastic facility location models. Mathematical Modelling, 3(5), 407–420.
Hakimi, S. L. (1964). Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research, 12(3), 450–459.
Lee, K. H. (2006). First course on fuzzy theory and applications (Vol. 27). Springer Science & Business Media.
Liu, B. & Liu, Y. K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE transactions on Fuzzy Systems, 10(4), 445-450.
Louveaux, F. V. (1986). Discrete stochastic location models. Annals of Operations Research, 6(2), 21–34.
O’Kelly, M. E. (1986). Activity levels at hub facilities in interacting networks. Geographical Analysis, 18(4), 343–356.
O’kelly, M. E. (1986). The location of interacting hub facilities. Transportation Science, 20(2), 92–106.
Saboury, A., Ghaffari-Nasab, N., Barzinpour, F., & Jabalameli, M. S. (2013). Applying two efficient hybrid heuristics for hub location problem with fully interconnected backbone and access networks. Computers & Operations Research, 40(10), 2493–2507.
Shahanaghi, K., Yavari, A., & Hamidi, M. (2015). Developing a model for Capacitated Hierarchical hub location with considering Delivery Time Restriction. Applied mathematics in Engineering, Management and Technology, 3(1), 540-548.
Toh, R. S. & Higgins, R. G. (1985). The impact of hub and spoke network centralization and route monopoly on domestic airline profitability. Transportation Journal, 24(4), 16-27.
Yaman, H. (2009). The hierarchical hub median problem with single assignment. Transportation Research Part B: Methodological, 43(6), 643–658.
Yaman, H., & Elloumi, S. (2012). Star p-hub center problem and star p-hub median problem with bounded path lengths. Computers & Operations Research, 39(11), 2725–2732.
Zadeh, L. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1(1978), 3-28.
Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
Zhu, H. & Zhang, J. (2009, November). A credibility-based fuzzy programming model for APP problem. In Artificial Intelligence and Computational Intelligence, 2009. AICI'09. International Conference on (Vol. 1, pp. 455-459). IEEE.