A Bi-objective Capacitated Single-Allocation Hub Location Problem with Reliability Assumption on Paths
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
F. Moeen Moghadas
1
,
F. Fuladi
2
1 - Department of Mathematics, University of Bojnord, Bojnord, Iran
2 - Department of Mathematics, University of Bojnord, Bojnord, Iran
کلید واژه: Bi-objective optimization, Capacitated hub, E-constraint, Hub location problem, Reliability of path,
چکیده مقاله :
The hub location problems are highly crucial due to their applications in the transportation and distribution area. Today, the complexities of solving the real world problems using the single-objective techniques are challenging. For a more real model, the present study considers a bi-objective capacitated single-allocation hub location problem assuming the reliability of paths. In addition to the capacity, the fixed costs for the hubs are considered, as well. Furthermore, while minimizing the cost, the reliability of the weakest path is making maximized. Three mathematical models are proposed for this problem. The performance of single-objective models is evaluated and then, the proposed bi-objective model is solved using the ε-constraint method. In the present study, the fixed cost is calculated using two different methods: one is based on the distance from the center of mass and another one depends on the hub capacity. The results reveal that the third model with the fixed cost based on the distance from the center of mass has the best performance.
مسائل مکان یابی هاب به دلیل کاربردهای بسیارشان در سیستم های حمل ونقل و توزیع از اهمیت بالایی برخوردار هستند. پیچیدگی های مسائل واقعی امروزی اغلب کاربرد مسائل تک هدفه را به چالش می کشاند. به منظور واقعی تر شدن مدل، در این مقاله مسئله دو هدفه مکان یابی پوشش هاب ظرفیت دار تک تخصیصی با در نظر گرفتن قابلیت اطمینان مسیرها مورد بررسی قرار می گیرد. در این مقاله علاوه بر ظرفیت برای هاب ها، هزینه های ثابتی نیز برای احداث آنها در نظرگرفته می شود. تلاش می شود همزمان با می نیمم سازی هزینه ها، امنیت ضعیف ترین مسیر شبکه نیز ماکسیمم شود. برای مسئله مفروض، سه مدل ریاضی پیشنهاد شده است. ابتدا عملکرد مدل های تک هدفه ارزیابی و پس از تعیین مدل مناسب تر، مدل دو هدفه پیشنهادی با استفاده از روش ε-محدودیت حل می شود. در این مقاله هزینه های ثابت احداث با دو روش متفاوت یکی براساس فاصله از مرکز جرم سیستم و دیگری بر اساس ظرفیت هاب ها محاسبه می شود. نتایج محاسباتی نشان می دهد که از میان سه مدل، سومین مدل ارائه شده و با هزینه های ثابت بر مبنای فاصله از مرکز جرم، دارای عملکرد بهتری است.
[1] S. Alumur, B.Y. Kara, Network hub location problems: the state of the art, European Journal of Opereration Research 190 (2008) 1-21.
[2] S. Anvari, M. Turkey, The facility location problem from the perspective of triple bottom line accounting of sustainability, International Journal of Production Research, http://dx.doi.org/10.1080/00207543.2017.1341064/.
[3] T. Aykin, Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem, European Journal of Opereration Research 79 (1994) 501-523.
[4] T. Aykin, Networking policies for hub-andspoke systems with applications to the air transportation system, Transportation Science 3 (1995) 201-221.
[5] N. Azizi, Managing facility disruption in hub-and-spoke networks: formulations and efficient solution methods, Annals Operational Research 272 (2019) 159-185.
[6] N. Azizi, S. Chauhan, S. Salhi, N. Vidyarthi, The impact of hub failure in hub-and-spoke networks: mathematical formulations and solution techniques, Computers Operations Research 65 (2016) 174-188.
[7] M. Bashiri, M. Rezanezhad, A reliable multi-objective p-hub covering location problem considering of hubs capabilities, IJE TRANSACTIONS B: Applications 28 (2015) 717-729.
[8] N. Boland, A. Ernst A, M. Krishnamoorthy, J. Ebery, Preprocessing and cutting methods for multiple allocation hub location problems, European Journal of Opereration Research 155 (2004) 638-653.
[9] R. S. Camargo, G. Miranda, Single allocation hub location problem under congestion: Network owner and user perspectives, Expert Systems with Applications 39 (2012) 3385-3391.
[10] R. S. Camargo, G. Miranda, R. P. M. Ferreira, A hybrid outer approximation/benders decomposition algorithm for the single allocation hub location problem under congestion, Operations Research Letters 39 (2011) 329-337.
[11] J. F. Campbell, Integer programming formulations of discrete hub location problems, European Journal of Opereration Research 72 (1994) 387-405.
[12] S. R. Cardoso, A. P. Barbosa-Pvoa, S. Relvas, A. Q. Novais, Resilience metrics in the assessment of complex supply-chains performance operating under demand uncertainty, Omega 56 (2015) 53-73.
[13] S. K. Chaharsooghia, F. Momayezia, N. Ghaffarinasab, An adaptive large neighborhood search heuristic for solving the reliable multiple allocation hub location problem under hub disruptions, International Journal of Industrial Engineering Computations 8 (2017) 191-202.
[14] J. F. Chen, A heuristic for the capacitated single allocation hub location problem, Advances in Industrial Engineering and Operations Research 5 (2008) 185-196.
[15] I. Contreras, J. A. Daz, E. Fernndez, Lagrangean relaxation for the capacitated hub location problem with single assignment, Operations Research spectrum 31 (2009) 483-505.
[16] I. Contreras, J. A. Diaz, E. Fernandez, Branch and price for large-scale capacitated hub location problems with single assignment, INFORMS Journal on Computing 23 (2011) 41-55.
[17] I. Correia, S. Nickel, F. Saldanha-da-Gama, Single-assignment hub location problems with multiple capacity levels, Transportation Research Part B 44 (2010) 1047-1066.
[18] I. Correia, S. Nickel, F. Saldanha-da-Gama, The capacitated single allocation hub location problem revisited: A note on a classical formulation, European Journal of Opereration Research 207 (2010) 92-96.
[19] M. Costa, M. Captivo, J. Climaco, Capacitated single allocation hub location problem, a bi-criteria approach, Computers tions Research 35 (2007) 3671-3695.
[20] K. Deb, Multi objective optimization using Evolutionary Algorithm, Wiley, New York, 2001.
[21] J. Ebery, M. Krishnamoorthy, A. Ernst, N. Boland, The capacitated multiple allocation hub location problem: formulations and algorithms, European Journal of Opereration Research 120 (2000) 614-631.
[22] A. Ebrahimi Zade, A. Sadegheih, M. Lotfi, A modified NSGA-II solution for a new multiobjective hub maximal covering problem under uncertain shipments, Journal of Industrial Engineering International 10 (2014) 185-197.
[23] M. Eghbali, M. Abedzadeh, M. Setak, Multiobjective reliable hub covering location considering customer convenience using NSGAII, International Journal of System Assurance Engineering and Management 5 (2014) 450-460.
[24] A. T. Ernst, M. Krishnamoorthy, Solution algorithms for the capacitated single allocation hub location problem, Annals of Operations Research 86 (1999) 141-159.
[25] M. H. Fazel Zarandi, S. Davari, A. H. Sisakht, Design of a reliable hub-and-spoke network using an interactive fuzzy goal programming, IEEE international conference on fuzzy systems (2011).
[26] S. Gelareh, D. Pisinger, Fleet deployment, network design and hub location of liner shipping companies, Transportation Research Part E: Logist Transport. Review 47 (2011) 947-964.
[27] R. Geramianfar, M. Pakzad, H. Golhashem, R. Tavakkoli-Moghaddam, A multi-objective hub covering location problem under congestion using simulated annealing algorithm, Uncertain Supply Chain Management 1 (2013) 153-164.
[28] V. Ghezavat, P. Hosseinifar, Application of efficient metaheuristics to solve a new biobjective optimization model for hub facility location problem considering value at risk criterion,Methodologies and Application , http://dx.doi.org/10.1007/s00500-016-2326-4/.
[29] N. Ghaffari-Nasab, Reliable hub-and-spoke network design problem with budget constraint, The 4th International Reliability Engineering Conference, IREC2016 (2016).
[30] A. Ghodratnama, H. R. Arbabi, A. Azaron, A biobjective hub locationallocation model considering congestion, Operational Research, http://dx.doi.org/10. 1007/s12351-018-0404-3/.
[31] Y. Haimes, D.A. Wismer, D. S. Lasdon, On a bicriterion formulation of the integrated systems identification and system optimization, IEEE Trans. Syst, Man Cybernet. 1 (1971) 296-297.
[32] H. Kim, M. E. O’Kelly, Reliable p-hub location problems in telecommunication networks, Geographical Analysis 41 (2009) 283-306.
[33] J. Kratica, M. Milanovic, Z. Stanimirovic, D. Tosic, An evolutionary-based approach for solving a capacitated hub location problem, Applied Soft Computing 11 (2011) 1858-1866.
[34] M. Labbe, H. Yaman, E. Gourdin, A branch and cut algorithm for the hub location problems with single assignment, Mathematical Programming 102 (2005) 371-405.
[35] C. C. Lin, S. C. Lee, The competition game on hub network design, Transport. Res. Part B.Transportation Research Part B 44 (2010) 618-629.
[36] R. F. Love, J. G. Morris, G. O. Wesolowsky, Facility Location: Models and Method, North Holland, New York, 1988.
[37] S. R. Madani, A. Shahandeh Nookabadi, S. R. Hejazi, A bi-objective, reliable single allocation p-hub maximal covering location problem: mathematical formulation and solution approach, Journal of Air Transport Management 68 (2018) 118-136.
[38] A. Marn, Formulating and solving splittable capacitated multiple allocation hub location problems, Computers Operations Research 32 (2005) 3093-3109.
[39] G. Mavrotas, Generation of efficient solutions in multi-objective mathematical programming problems using GAMS, effective implementation of the -constraint method, www.gams.com/modlib/adddocs/epscm.pdf, 2008.
[40] G. Mavrotas, K. Florios, An improved version of the augmented -constraint method for finding the exact pareto set in multiobjective integer programming problems, Applied Mathematics and Computation 219 (2013) 9652-9669.
[41] M. Mohammadi, R. Tavakkoli-Moghaddam, A. Siadat, J. Dantan, Design of a reliable logistics network with hub disruptions under uncertainty, Applied Mathematical Modeling, http://dx.doi.org/10.1016/j.apm. 2016.01.011/.
[42] M. Mohammadi, R. Tavakkoli-Moghaddam, A. Siadat, Y. Rahimi, A game-based metaheuristic for a fuzzy bi-objective reliable hub location problem, Engineering Applications of Artificial Intelligence 50 (2016) 1-19.
[43] M. M. Nasiri, N. Shamsi Gamchi, S. A. Torabi, Cuckoo Optimization Algorithm for a reliable Location-allocation of Hubs among the clients, International Journal of Industrial Engineering Production Research 27 (2016) 309-320.
[44] M. E. Okelly, A quadratic integer program for the location of interacting hub facilities, European Journal of Operational Research 32 (1987) 393-404.
[45] M. E. Okelly, Hub facility location with fixed costs, Regional Science 71 (1992) 293-306.
[46] F. Parvaresh, S. M. M. Husseini, S. A. H. Golpayegany, Hub network design problem in the presence of disruptions, Journal of Intelligent Manufacturing 25 (2014) 755-774.
[47] H. R. Pasandideh, T. Akhavan Niaki, M. A. Sheikhi, A bi-objective hub maximal covering location problem considering timedependent reliability and the second type of coverage, International Journal of Management Science and Engineering Management 11 (2016) 195-202.
[48] M. Randall, Solution approaches for the capacitated single allocation hub location problem using ant colony optimization, Computational Optimization and Applications 39 (2008) 239-261.
[49] I. Rodriguez-Martin, J. J. Salazar-Gonzalez, Solving a capacitated hub location problem, European Journal of Operational Research 184 (2008) 468-479.
[50] B. Rostami, N. Kmmerling, C. Buchheim, U. Clausen, Reliable single allocation hub location problem under hub breakdowns, Computers and Operations Research 96 (2018) 15-29.
[51] S. Sadat Torkestani, S. M. Seyedhosseini, A. Makui, K. Shahanaghi, The reliable design of a hierarchical multi-modes transportation hub location problems (HMMTHLP) under dynamic network disruption (DND), Computers Industrial Engineering 122 (2018) 39-86.
[52] M. Sadeghi, R. Tavakkoli-Moghaddam, An efficient imperialism competitive algorithm for a reliable hub covering location problem, International Journal of Machine Learning and Computing 5 (2015) 40-43.
[53] M. Sasaki, M. Fukushima, On the hub-andspoke model with arc capacity constraints, Journal of the Operations Research Society of Japan 46 (2003) 409-428.
[54] R. Tavakoli-Moghadam, M. Alinaghian, N. Norouzi, A. SalamatBakhsh, Solving a new vehicle routing problem considering safety in hazardous materials transportation, Journal of Transportation Research 2 (2012) 223-237.
[55] T. H. Tran, J. R. OHanley, M. P. Scaparra, Reliable hub network design: formulation and solution techniques, Transportation Science 51 (2016) 358-367.
[56] R. Zanjirani Farahani, M. Hekmatfar, A.
Boloori Arabani, E. Nikbakhsh, Hub location problems: A review of models, classification, solution techniques, and applications, Computers Industrial Engineering 64
(2013) 1096-1109.
[57] M. Zhalechian, S. Ali Torabi, M. Mohammadi, Hub-and-spoke network design under
operational and disruption risks, Transportation Research: Part E 109 (2018) 20-43.
