Decentralized Fuzzy P-hub Centre Problem: Extended Model and Genetic Algorithms

Document Type: Research Paper


Department of industrial engineering, Islamic Azad University of Karaj, Karaj, Iran


This paper studies the uncapacitated P-hub center problem in a network under decentralized management assuming time as a fuzzy variable. In this network, transport companies act independently, each company makes its route choices according to its own criteria. In this model, time is presented by triangular fuzzy number and used to calculate the fraction of users that probably choose hub routes instead of direct routes. To solve the problem, two genetic algorithms are proposed. The computational results compared with LINGO indicate that the proposed algorithm solves large-scale instances within promising computational time and outperforms LINGO in terms of solution quality.


Main Subjects

Alumur S. A., Kara B. Y., and Karasan O. E. (2012). Multimodal hub location and hub network design, Omega,Vol. 40(6), pp. 927–939.

Bashiri M., Mirzaei M. and Randall M. (2013). Modeling fuzzy capacitated p-hub center problem and a genetic algorithm solution, Applied Mathematical Modelling,Vol. 37, pp. 3513–3525.

Campbell JF. and O’Kelly ME. (2012). Twenty-five years of hub location research, Transp Sci, Vol.46, pp. 153–169.

Campbell J.F., Miranda J.R., Camargo R.S. and O’Kelly M.E. (2015). Hub Location and Network Design with Fixed and Variable Costs. Annual Hawaii International Conference on System Sciences, Computer Society Press,No. 48, pp. 1059-1067.

Contreras I., Cordeau J.F. and Laporte G. (2011). Benders Decomposition for Large-Scale Uncapacitated Hub Location, operation research, Vol.6, pp. 1477-1490.

Doerner K.F., Gendreau M., Greistorfer P., Gutjahr W., Hartl RF., and Reimann M. (2007). Metaheuristics-progress in complex systems optimization, Berlin: Springer.

Domencich T. and McFadden D.L. (1975). Urban travel demand: a behavioral analysis, Amsterdam: North-Holland Publishing Co.

Eraslan S. (2010). A genetic algorithm for the p-hub center problem with stochastic service level constraints, Dissertation, Middle East technical university.

Ghaderi A. and Jabalameli M.S. (2013). Modeling the budget-constrained dynamic uncapacitated facility location–network design problem and solving it via two efficient heuristics: a case study of health care, Math Comput Model, Vol.57, pp. 382–400.

Goldberg D.E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning, Reading, MA: Addison-Wesley.

Haupt R.L. and Haupt S.E. (2004). Practical Genetic Algorithms, New York: Wiley.

Hernández P., Alonso-Ayuso A., Bravo F., Escudero LF., Guignard M., Marianov V., and Weintraub A. (2012). A branch-and-cluster coordination scheme for selecting prison facility sites under uncertainty, Comput Oper Res, Vol.39, pp. 2232–2241.

Holland J.H. (1975). Adaptation in natural and artificial systems, Michigan: University of Michigan Press.

Hult E., Jiang H. and Ralph D. (2014). Exact computational approaches to a stochastic uncapacitated single allocation p-hub center problem, Computational Optimization and Applications, Vol.59, pp. 85-200.

Kaur A. and Kumar A. (2011). A new method for solving fuzzy transportation problems using ranking function, Applied Mathematical Modeling, Vol.35, pp. 5652–5661.

Kratica J., Stanimirović Zorica., Tosic D. and Filipović. (2005). Genetic algorithm for solving uncapacitated multiple allocation hub location problems, Computing and Informatics, Vol.24, pp. 415–426.

Kwang D.r. and Lee H. (2005). First Course on Fuzzy Theory and Applications, Berlin: Springer.

Nematian J. and Musavi M. (2016). Uncapacitated phub center problem under uncertainty, Journal of Industrial and Systems engineering (Iranian Institute of Industrial Engineering) ,Vol. 9, pp. 23-39.

O’Kelly M.E., Campbell J.F., Camargo R.S. and Miranda J.R. (2014). Multiple Allocation Hub Location Model with Fixed Arc Costs, Geographical Analysis, Vol.47, pp. 73–96.

Ortuzar J.D. and Willumsen L.G. (1995). Modelling transport, New York, Wiley.

Qin Z. and Gao Y. (2014). Uncapacitated p-hub location problem with fixed costs and uncertain flows, Journal of Intelligent Manufacturing, pp. 1-12.

Rabbani M. and Kazemi M. (2015). Solving uncapacitated multiple allocation p-hub center problem by Dijkstra’s algorithm-based genetic algorithm and simulated annealing, International Journal of Industrial Engineering Computations, Vol.6, pp. 405–418.

Rahmaniani R., Saidi M. and Ashouri H. (2013a). Robust Capacitated Facility Location Problem: Optimization Model and Solution Algorithms, J Uncertain Syst Vol.7(1), pp. 22–35.

Rahmaniani R., Ghaderi A., Mahmoudi N. and Barzinepour S. (2013b). Stochastic p–robust uncapacitated multiple allocation p–hub location problems, Int J Ind Syst Eng Vol.14, pp. 296–314.

Topcuoglu H., Corut F., Ermis M. and Yilmaz G. (2005). Solving the uncapacitated hub location using genetic algorithms, Computers and Operational Research, Vol.32, pp. 467–984.

Vasconcelos A.D., Nassi C.D. and Lopes L.S. (2011). The uncapacitated hub location problem in networks under decentralized management, Computers & Operations Research, Vol.38, pp. 1656–1666.

Waldemiro P.N. and Widmer J. (2013). Compatibility of Long and Heavy Cargo Vehicles With the Geometric Design Standards of Brazilian Rural Roads and Highways, New York: Wiley.

Yang K., Liu Y.K. and Zhang X. (2011). Stochastic p-hub center problem with discrete time distributions, Lecture Notes, Computer Science, Vol.6676, pp. 182–191.

Yang K., Liu Y.K. and Yang G.Q. (2013). Solving fuzzy p-hub center problem by genetic algorithm incorporating local search, Applied Soft Computing, Vol.13(5), pp. 2624–2632.

Zarrinpoor N. and Seifbarghy M. (2011). A competitive location model to obtain a specific market share while ranking facilities by shorter travel time, Int J Adv Manuf Technol Vol.55, pp. 807–816.

Zanjirani Farahani R. , Hekmatfar M., Boloori Arabani A. and Nikbakhsh E. (2013). Hub location problems: A review of models, classification, solution techniques, and applications, Computers & Industrial Engineering, Vol.64, pp. 1096–1109.