Abstract
This study introduces a new problem for uncapacitated single allocation hub location in which pricing is taken into account. The objective is profit maximization by choosing the best hub and spoke topology and applying the optimal pricing, in the case of price-dependent demand. It is assumed that the source determining the number of hubs is endogenous. Two variants of the considered problem are addressed: deterministic and robust. For the initial non-linear model, we show how the deterministic variant can be reformulated as a mixed-integer linear program, excluding the price variables. In the robust counterpart case, the quantity of commodity flows between the pairs of customers is of stochastic nature. The goal of the robust variant is to design a hub and spoke network, together with the pricing structure, that would be immune to small perturbations of demand. Starting from the original model for the robust case, we have shown how to formulate an equivalent mixed-integer conic-quadratic program. In addition, we have proposed a 2-phase matheuristic approach for the robust variant. A computational study was conducted on the set of hub instances from the literature using the commercial state-of-the-art solver. The obtained computational results are thoroughly discussed, location patterns are analyzed and some managerial insights are provided. The experimental study also showed that the proposed matheuristic approach for the robust variant performs better compared to the commercial solver.
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References
Aboolian R, Berman O, Krass D (2008) Optimizing pricing and location decision for competitive service facilities charging uniform price. J Oper Res Soc 59:1506–1519. https://doi.org/10.1057/palgrave.jors.2602493
Alumur S, Kara B (2008) Network hub location problems: the state of the art. Eur J Oper Res 190(1):1–21. https://doi.org/10.1016/j.ejor.2007.06.008
Alumur S, Nickel S, Saldanha-de-Gama F (2012) Hub location under uncertainty. Transport Res B 46(4):529–543
Alumur SA, Nickel S, Rohrbeck B, Saldanha-da-Gama F (2018) Modeling congestion and service time in hub location problems. Appl Math Model 55:13–32
Boukani FH, Moghaddam BF, Pishvaee MS (2016) Robust optimization approach to capacitated single and multiple allocation hub location problems. Comput Appl Math 35:45–60. https://doi.org/10.1007/s40314-014-0179-y
Calik H, Alumur SA, Kara BY, Karasan OE (2009) A tabu-search based heuristic for the hub covering problem over incomplete hub networks. Comput Oper Res 36(12):3088–3096
Campbell J, O’Kelly M (2012) Twenty-five years of hub location research. Transport Sci 46(2):153–169. https://doi.org/10.1287/trsc.1120.0410
Chen X, Sim M, Sun P (2007) A robust optimization perspective on stochastic programming. Oper Res 55(6):1058–1071
Contreras I (2015) Hub location problems. In: Laporte G, Nickel S, Saldanha da Gama F (eds) Location science. Springer, Cham, pp 311–344. https://doi.org/10.1007/978-3-319-13111-5_12
Contreras I, Cordeau J, Laporte G (2011) Stochastic uncapacitated hub location. Eur J Oper Res 212:518–528
Elhedhli S, Wu H (2010) A Lagrangian heuristic for hub-and-spoke system design with capacity selection and congestion. Inf J Comput 22:282–296
Farahani R, Hekmatfar M, Arabani A, Nikbakhsh E (2013) Hub location problems: a review of models, classification, solution techniques, and applications. Comput Ind Eng 64(4):1096–1109. https://doi.org/10.1016/j.cie.2013.01.012
Fernández J, Salhi S, Toth B (2014) Location equilibria for continuous competitive facility location problem under delivered pricing. Comput Oper Res 41:185–195. https://doi.org/10.1016/j.cor.2013.08.004
Gülpinar N, Pachamanova D, Canakoglu E (2013) Robust strategies for facility location under uncertainty. Eur J Oper Res 225(1):21–35
Jeong SJ, Lee CG, Bookbinder JH (2007) The European freight railway system as a hub-and-spoke network. Transport Res A 41(6):523–536
Koksalan M, Soylu B (2010) Bicriteria p-hub location problems and evolutionary algorithms. Inf J Comput 22:191–205
Küçükaydin H, Aras N, Kuban Altinel İ (2012) A leader-follower game in competitive facility location. Comput Oper Res 39(2):437–448. https://doi.org/10.1016/j.cor.2011.05.007
Lüer-Villagra A, Marianov V (2013) A competitive hub location and pricing problem. Eur J Oper Res 231(3):734–744
Marianov V, Serra D (2003) Location models for airline hubs behaving as M/D/c queues. Comput Oper Res 30(7):983–1003
Martins de Sá E, Morabito R, De Camargo RS (2018) Efficient Benders decomposition algorithms for the robust multiple allocation incomplete hub location problem with service time requirements. Expert Syst Appl 93:50–61
Merakli M, Yaman H (2016) Robust intermodal hub location under polyhedral demand uncertainty. Transport Res B Methods 86:66–85
Mišković S, Stanimirović Z (2017) A hybrid metaheuristic method for the deterministic and robust uncapacitated multiple allocation p-hub centre problem. Eur J Ind Eng 11(5):631–662
Mohammadi J, Jolai F, Rostami H (2011) An M/M/c queue model for hub covering location problem. Math Comput Model 54(11–12):2623–2638
O’Kelly M (1987) A quadratic integer program for the location of interacting hub facilities. Eur J Oper Res 32:393–404
O’Kelly ME, Luna HPL, de Camargo RS, Miranda G (2015) Hub location problems with price sensitive demands. Netw Spat Econ 15(4):917–945
Panin A, Pashchenko M, Plyasunov A (2014) Bilevel competitive facility location and pricing problems. Autom Remote Control 75(4):715–727. https://doi.org/10.1134/S0005117914040110
Shahabi M, Unnikrishnan A (2014) Robust hub network design problem. Transport Res E Log 70:356–373. https://doi.org/10.1016/j.tre.2014.08.003
Snyder L (2006) Facility location under uncertainty: a review. IIE Trans 38:537–554
Talbi E-G, Todosijević R (2017) The robust uncapacitated multiple allocation p-hub median problem. Comput Ind Eng 110:322–332
Tikani H, Honarvar M, Mehrjerdi YZ (2018) Developing an integrated hub location and revenue management model considering multi-classes of customers in the airline industry. Comput Appl Math 37(3):3334–3364. https://doi.org/10.1007/s40314-017-0512-3
Wagner M, Bhadury J, Peng S (2009) Risk management in uncapacitated facility location models with random demands. Comput Oper Res 36(14):1002–1011
Zetina CA, Contreras I, Cordeau JF, Nikbakshsh E (2017) Robust uncapacitated hub location. Transport Res B Methods 106:393–410
Acknowledgements
This research was partially supported by Serbian Ministry of Education, Science and Technological Development under the Grant no. 174010. We are grateful to the two anonymous reviewers for valuable and constructive comments that have helped us to improve our work.
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Communicated by Hector Cancela.
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Čvokić, D.D., Stanimirović, Z. A single allocation hub location and pricing problem. Comp. Appl. Math. 39, 40 (2020). https://doi.org/10.1007/s40314-019-1025-z
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DOI: https://doi.org/10.1007/s40314-019-1025-z