Abstract
The hub covering problem can be viewed as a combination of the set covering and the hub location problem. In a traditional hub covering problem, all parameters are assumed to be deterministic. However, neglecting uncertainties associated with demand and transportation costs may lead to inferior solutions. Thus, we introduce three novel stochastic optimization models to formulate a multiple allocation hub covering problem in which deterministic transportation cost and demand assumptions are relaxed. Further, we also reflect scale economy to the models via inter-hub transportation cost discount factor. The L-Shaped Algorithm is applied to solve the sculpted problems. To test the efficiency of the proposed models, several test instances are generated and solved based on simulated data. The effects of the change of coverage radius, inter-hub discount factor, and hub opening cost are also examined. Results of this study validate that modeling the hub covering problem as a stochastic optimization model yields up 13.05\(\%\) efficiency when compared to the expectation of the expected value method.
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References
Alumur, S., & Kara, B. Y. (2008). Network hub location problems: The state of the art. European Journal of Operational Research, 190(1), 1–21.
Alumur, S. A., & Kara, B. Y. (2009). A hub covering network design problem for cargo applications in Turkey. The Journal of the Operational Research Society, 60(10), 1349–1359.
Alumur, S. A., Nickel, S., & da Gama, F. S. (2012). Hub location under uncertainty. Transportation Research Part B: Methodological, 46(4), 529–543.
Azizi, N., Vidyarthi, N., & Chauhan, S. (2018). Modelling and analysis of hub-and-spoke networks under stochastic demand and congestion. Annals of Operations Research, 264, 1–40.
Beasley, J. (1990). Or-library. Retrieved February 4, 2022 from http://people.brunel.ac.uk/mastjjb/jeb/orlib/files/phub4.txt
Birge, J. R., & Louveaux, F. (2011). Introduction to stochastic programming (2nd ed.). New York: Springer.
Bozorgi-Amiri, A., & Khorsi, M. (2016). A dynamic multi-objective location-routing model for relief logistic planning under uncertainty on demand, travel time, and cost parameters. The International Journal of Advanced Manufacturing Technology, 85, 1633–1648.
Campbell, J. F. (1994). Integer programming formulations of discrete hub location problems. European Journal of Operational Research, 72(2), 387–405.
Campbell, J. F., & O’Kelly, M. E. (2012). Twenty-five years of hub location research. Transportation Science,46(2), 153–169.
Contreras, I. (2015). Hub location problems (pp. 311–344). Cham: Springer.
Contreras, I., Cordeau, J. F., & Laporte, G. (2011). Stochastic uncapacitated hub location. European Journal of Operational Research, 212(3), 518–528.
Correia, I., Nickel, S., & da Gama, F. S. (2018). A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities. Omega, 74, 122–134.
Ernst, A. T., & Krishnamoorthy, M. (1998). Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem. European Journal of Operational Research, 104(1), 100–112.
Ernst, A., & Krishnamoorthy, M. (1999). Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research, 86, 141–159.
Gurobi Optimization L (2020) Gurobi optimizer reference manual. Retrieved February 4, 2022 from http://www.gurobi.com
Habibi, M. K., Allaoui, H., & Goncalves, G. (2018). Collaborative hub location problem under cost uncertainty. Computers & Industrial Engineering, 124, 393–410.
Hamacher, H. W., Labbé, M., Nickel, S., & Sonneborn, T. (2004). Adapting polyhedral properties from facility to hub location problems. Discrete Applied Mathematics, 145(1), 104–116.
Hatefi, M., Jolai, F., Torabi, S., & Tavakkoli-Moghaddam, R. (2015). Reliable design of an integrated forward-revere logistics network under uncertainty and facility disruptions: A fuzzy possibilistic programing model. KSCE Journal of Civil Engineering, 19, 1117–1128.
Hult, E., Jiang, H., & Ralph, D. (2013). Exact computational approaches to a stochastic uncapacitated single allocation p-hub center problem. Computational Optimization and Applications, 59(1), 185–200.
Karatas, M. (2020). A multi-objective bi-level location problem for heterogeneous sensor networks with hub-spoke topology. Computer Networks, 181, 107551.
Karatas, M., & Onggo, B. S. (2019). Optimising the barrier coverage of a wireless sensor network with hub-and-spoke topology using mathematical and simulation models. Computers & Operations Research, 106, 36–48.
Lowe, T. J., & Sim, T. (2013). The hub covering flow problem. The Journal of the Operational Research Society, 64(7), 973–981.
Merakli, M., & Yaman, H. (2017). A capacitated hub location problem under hose demand uncertainty. Computers and Operations Research, 88, 58–70.
O’Kelly, M. E. (1987). A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research,32(3), 393–404.
O’Kelly, M. E. (1992). Hub facility location with fixed costs. Papers in Regional Science,71(3), 293–306.
Qin, Z., & Gao, Y. (2017). Uncapacitated \(p\)-hub location problem with fixed costs and uncertain flows. Journal of Intelligent Manufacturing, 28(3), 705–716.
Sadeghi, M., Jolai, F., Tavakkoli-Moghaddam, R., & Rahimi, Y. (2015). A new stochastic approach for a reliable p-hub covering location problem. Computer and Industrial Engineering, 90, 371–380.
Sener, N., & Feyzioglu, O. (2021). Capacitated hub covering flow problem. Manas Journal of Engineering, 9(1), 72–84.
Shang, X., Yang, K., Wang, W., Wang, W., Zhang, H., & Celic, S. (2020). Stochastic hierarchical multimodal hub location problem for cargo delivery systems: Formulation and algorithm. IEEE Access, 8, 55076–55090.
Sim, T., Lowe, T. J., & Thomas, B. W. (2009). The stochastic hub center problem with service-level constraints. Computers & Operations Research, 36(12), 3166–3177.
Slyke, R. M. V., & Wets, R. (1969). L-shaped linear programs with applications to optimal control and stochastic programming. SIAM Journal on Applied Mathematics, 17(4), 638–663.
Snyder, L. V. (2006). Facility location under uncertainty: a review. IIE Transactions, 38(7), 547–564.
Taherkhani, G., Alumur, S. A., & Hosseini, M. (2020). Benders decomposition for the profit maximizing capacitated hub location problem with multiple demand classes. Transportation Science, 54(6), 1446–1470.
Train, J., Etefia, B., & Green, H. (2010). Hub and spoke bgp: Leveraging multicast to improve wireless inter-domain routing. In: 2010 IEEE Aerospace Conference (pp. 1–7)
Yahyaei, M., & Bashiri, M. (2017). Scenario-based modeling for multiple allocation hub location problem under disruption risk: Multiple cuts benders decomposition approach. Journal of Industrial Engineering International, 13, 445–453.
Yang, T. H. (2009). Stochastic air freight hub location and flight routes planning. Applied Mathematical Modelling, 33(12), 4424–4430.
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The authors would like to express the deepest appreciation to the editor and the anonymous reviewers for their invaluable remarks that help us to improve the first version of the paper.
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Sener, N., Feyzioglu, O. Multiple allocation hub covering flow problem under uncertainty. Ann Oper Res 320, 975–997 (2023). https://doi.org/10.1007/s10479-022-04553-2
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DOI: https://doi.org/10.1007/s10479-022-04553-2