Document Type : Article

**Authors**

School of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran.

**Abstract**

In the most past hub location problem (HLP) studies, failure probability is limited to a constant value; while in reality, it depends on various factors including natural disasters such as floods and earthquakes, commodity flow, institutional elements such as strikes, and etc. This paper looks into the problem of hub network design through a new model. The problem is to maximize the network reliability and to minimize the total routing cost simultaneously. In order to provide a more realistic model, the hub’s failure probabilities were considered as a function of the hub’s incoming traffic. Reserve hub elements are also taken into account in the model with the aim of increasing network reliability. To solve the model, a non-dominated sorting genetic algorithm (NSGA-II) is presented. The parameters of the algorithm are tuned using Taguchi method. The proposed solution is then carried out in a case study where the results confirm the acceptable performance of the model and also sensitivity analysis is performed in order to describe the effects of critical parameters into objective functions.

**Keywords**

**Main Subjects**

References:

1. Sim, T.K.T. "The hub covering flow problem and the stochastic p-hub center problem", PhD Thesis, University of Iowa (2007).

2. Kim, H. and O'Kelly, M.E. "Reliable p-hub location problems in telecommunication networks", Geographical Analysis, 41(3), pp. 283-306 (2009). DOI: 10.1111/j.1538-4632.2009.00755.x.

3. Davari, S., Fazel, M.H., and Turksen, I. "The fuzzy reliable hub location problem", Fuzzy Information Processing Society (NAFIPS), 2010 Annual Meeting of the North American Fuzzy Information Processing Society: IEEE, pp. 1-6 (2010). DOI:

10.1109/NAFIPS.2010.5548271.

4. Fazel, M.H., Davari, S., and Haddad Sisakht, S.A. "The Q-coverage multiple allocation hub covering problem with mandatory dispersion", Scientia Iranica, 19(3), pp. 902-911 (2012). DOI: 10.1016/j.scient.2012.03.007.

5. Karimi, H. and Bashiri, M. "Hub covering location problems with different coverage types", Scientia Iranica, 18(6), pp. 1571-1578 (2011). DOI: 10.1016/j.scient.2011.09.018.

6. Hamidi, M., Gholamian, M.R., and Shahanaghi, K. "Developing prevention reliability in hub location models", Journal of Risk and Reliability, 228(4), pp. 337-346 (2014). DOI: 10.1177/1748006X13519247.

7. Yaman, H. "The hierarchical hub median problem with single assignment", Transportation Research Part B: Methodological, 43(6), pp. 643-58 (2009). DOI:10.1016/j.trb.2009.01.005.

8. Hamzaoui, S. and Ben-Ayed, O. "Parcel distribution timetabling problem", Operations Management Research, 4(3-4), pp. 138-149 (2011). DOI:10.1007/s12063-011-0056-4.

9. Yaman, H. and Elloumi, S. "Star p-hub center problem and star p-hub median problem with bounded path lengths", Computers and Operations Research, 39(11), pp. 2725-2732 (2012). DOI: 10.1016/j.cor.2012.02.005.

10. Alumur, S.A., Yaman, H., and Kara, B.Y. "Hierarchical multimodal hub location problem with timede finite deliveries", Transportation Research Part E: Logistics and Transportation Review, 48(6), pp. 1107- 1120 (2012). DOI: 10.1016/j.tre.2012.04.001.

11. Davari, S. and Fazel, M.H. "The single-allocation hierarchical hub-median problem with fuzzy flows", Advances in Intelligent Systems and Computing, 195, Springer, pp. 165-181 (2013). DOI: 10.1007/978-3-642- 33941-7 17.

12. Fazel, M.H., Davari, S., and Haddad Sisakht, S.A. "An empirical comparison of simulated annealing and iterated local search for the hierarchical single allocation hub median location problem", Scientia Iranica, 22(3), pp. 1203-1217 (2015).

13. Zhong, W., Juan, Z., Zong, F., et al. "Hierarchical hub location model and hybrid algorithm for integration of urban and rural public transport", International Journal of Distributed Sensor Networks, 14(4) (2018). DOI: 10.1177/1550147718773263.

14. Smith, H., Cakebread, D., Battarra, M., et al. "Location of a hierarchy of HIV/AIDS test laboratories in an inbound hub network: case study in South Africa", Journal of the Operational Research Society, 68(9), pp. 1068-1081 (2017). DOI: 10.1057/s41274-017-0240-5.

15. Sedehzadeh, S., Tavakkoli-Moghaddam, R., Baboli, A., et al. "Optimization of a multi-modal tree hub location network with transportation energy consumption: A fuzzy approach", Journal of Intelligent and Fuzzy Systems, 30(1), pp. 43-60 (2016). DOI: 10.3233/IFS-151709.

16. Korani, E. and Sahraeian, R. "The hierarchical hub covering problem with an innovative allocation procedure covering radiuses", Scientia Iranica, 20(6), pp. 2138-2160 (2013).

17. Li, T.-T., Song, R., He, S.-W., et al. "Optimization model of comprehensive passenger hub in urban agglomeration based on hierarchical layout", China Journal of Highway and Transport, 29(2), pp. 116-122 (2016).

18. Li, T.-T., Song, R., He, S.-W., et al. "Multiperiod hierarchical location problem of transit hub in urban agglomeration area", Mathematical Problems in Engineering, online (2017). DOI: 10.1155/2017/7189060.

19. Dukkanci, O. and Kara, B.Y. "Routing and scheduling decisions in the hierarchical hub location problem", Computers and Operations Research, 85, pp. 45-57 (2017). DOI: 10.1016/j.cor.2017.03.013.

20. Ryerson, M.S. and Kim, H. "Integrating airline operational practices into passenger airline hub definition", Journal of Transport Geography, 31, pp. 84-93 (2013). DOI: 10.1016/j.jtrangeo.2013.05.013.

21. Karimi, M., Eydi, A.R., and Korani, E. "Modeling of the capacitated single allocation hub location problem with a hierarchical approach", International Journal of Engineering, Transactions A: Basics, 27(4), pp. 573- 586 (2014).

22. Esmizadeh, Y. and Bashiri, M. "Applying hierarchical hub location problem on perishable good distribution systems", Joint International Symposium on The Social Impacts of Developments in Information, Manufacturing and Service Systems, Istanbul, Turkey, pp. 260-269 (2014).

23. Da Costa Fontes, F.F. and Goncalves, G. "Routing problem with pendular and cyclic service in a hierarchical structure of hub and spoke with multiple allocation of sub-hubs", International Conference on Industrial Engineering and Systems Management, Seville, Spain, pp. 561-567 (2015). DOI: 10.1109/IESM.2015.7380214.

24. Mahmutogullari, A.I. and Kara, B.Y. "Hub location under competition", European Journal of Operational Research, 250(1), pp. 214-225 (2016). DOI: 10.1016/j.ejor.2015.09.008.

25. Kim, J., Lee, S., and Lee, S. "An evacuation route choice model based on multi-agent simulation in order to prepare Tsunami disasters", Transportmetrica B: Transport Dynamics, 5(4), pp. 385-401 (2017). DOI: 10.1080/21680566.2016.1147002.

26. Torkestani, S., Seyedhosseini, S.M., Makui, A., et al. "The reliable design of a hierarchical multi-modes transportation hub location problems (HMMTHLP) under dynamic network disruption (DND)", Computers & Industrial Engineering, 122, pp. 39-86 (2018). DOI: 10.1016/j.cie.2018.05.027.

27. Cohon, J.L., Multi-Objective Programming and Planning, Chapter 6.2, 2nd Edn., Dover Publications (2013).

28. Ernest, A.T. and Krishnamoorthy, M. "Efficient algorithms for the uncapacitated single allocation-hub median problem", Location Science, 4(3), pp. 139-54 (1996). DOI: 10.1016/S0966-8349(96)00011-3.

29. Schott, J.R. "Fault tolerant design using single and multicriteria genetic algorithm optimization", Master's Thesis, MIT University (1995).

2. Kim, H. and O'Kelly, M.E. "Reliable p-hub location problems in telecommunication networks", Geographical Analysis, 41(3), pp. 283-306 (2009). DOI: 10.1111/j.1538-4632.2009.00755.x.

3. Davari, S., Fazel, M.H., and Turksen, I. "The fuzzy reliable hub location problem", Fuzzy Information Processing Society (NAFIPS), 2010 Annual Meeting of the North American Fuzzy Information Processing Society: IEEE, pp. 1-6 (2010). DOI:

10.1109/NAFIPS.2010.5548271.

4. Fazel, M.H., Davari, S., and Haddad Sisakht, S.A. "The Q-coverage multiple allocation hub covering problem with mandatory dispersion", Scientia Iranica, 19(3), pp. 902-911 (2012). DOI: 10.1016/j.scient.2012.03.007.

5. Karimi, H. and Bashiri, M. "Hub covering location problems with different coverage types", Scientia Iranica, 18(6), pp. 1571-1578 (2011). DOI: 10.1016/j.scient.2011.09.018.

6. Hamidi, M., Gholamian, M.R., and Shahanaghi, K. "Developing prevention reliability in hub location models", Journal of Risk and Reliability, 228(4), pp. 337-346 (2014). DOI: 10.1177/1748006X13519247.

7. Yaman, H. "The hierarchical hub median problem with single assignment", Transportation Research Part B: Methodological, 43(6), pp. 643-58 (2009). DOI:10.1016/j.trb.2009.01.005.

8. Hamzaoui, S. and Ben-Ayed, O. "Parcel distribution timetabling problem", Operations Management Research, 4(3-4), pp. 138-149 (2011). DOI:10.1007/s12063-011-0056-4.

9. Yaman, H. and Elloumi, S. "Star p-hub center problem and star p-hub median problem with bounded path lengths", Computers and Operations Research, 39(11), pp. 2725-2732 (2012). DOI: 10.1016/j.cor.2012.02.005.

10. Alumur, S.A., Yaman, H., and Kara, B.Y. "Hierarchical multimodal hub location problem with timede finite deliveries", Transportation Research Part E: Logistics and Transportation Review, 48(6), pp. 1107- 1120 (2012). DOI: 10.1016/j.tre.2012.04.001.

11. Davari, S. and Fazel, M.H. "The single-allocation hierarchical hub-median problem with fuzzy flows", Advances in Intelligent Systems and Computing, 195, Springer, pp. 165-181 (2013). DOI: 10.1007/978-3-642- 33941-7 17.

12. Fazel, M.H., Davari, S., and Haddad Sisakht, S.A. "An empirical comparison of simulated annealing and iterated local search for the hierarchical single allocation hub median location problem", Scientia Iranica, 22(3), pp. 1203-1217 (2015).

13. Zhong, W., Juan, Z., Zong, F., et al. "Hierarchical hub location model and hybrid algorithm for integration of urban and rural public transport", International Journal of Distributed Sensor Networks, 14(4) (2018). DOI: 10.1177/1550147718773263.

14. Smith, H., Cakebread, D., Battarra, M., et al. "Location of a hierarchy of HIV/AIDS test laboratories in an inbound hub network: case study in South Africa", Journal of the Operational Research Society, 68(9), pp. 1068-1081 (2017). DOI: 10.1057/s41274-017-0240-5.

15. Sedehzadeh, S., Tavakkoli-Moghaddam, R., Baboli, A., et al. "Optimization of a multi-modal tree hub location network with transportation energy consumption: A fuzzy approach", Journal of Intelligent and Fuzzy Systems, 30(1), pp. 43-60 (2016). DOI: 10.3233/IFS-151709.

16. Korani, E. and Sahraeian, R. "The hierarchical hub covering problem with an innovative allocation procedure covering radiuses", Scientia Iranica, 20(6), pp. 2138-2160 (2013).

17. Li, T.-T., Song, R., He, S.-W., et al. "Optimization model of comprehensive passenger hub in urban agglomeration based on hierarchical layout", China Journal of Highway and Transport, 29(2), pp. 116-122 (2016).

18. Li, T.-T., Song, R., He, S.-W., et al. "Multiperiod hierarchical location problem of transit hub in urban agglomeration area", Mathematical Problems in Engineering, online (2017). DOI: 10.1155/2017/7189060.

19. Dukkanci, O. and Kara, B.Y. "Routing and scheduling decisions in the hierarchical hub location problem", Computers and Operations Research, 85, pp. 45-57 (2017). DOI: 10.1016/j.cor.2017.03.013.

20. Ryerson, M.S. and Kim, H. "Integrating airline operational practices into passenger airline hub definition", Journal of Transport Geography, 31, pp. 84-93 (2013). DOI: 10.1016/j.jtrangeo.2013.05.013.

21. Karimi, M., Eydi, A.R., and Korani, E. "Modeling of the capacitated single allocation hub location problem with a hierarchical approach", International Journal of Engineering, Transactions A: Basics, 27(4), pp. 573- 586 (2014).

22. Esmizadeh, Y. and Bashiri, M. "Applying hierarchical hub location problem on perishable good distribution systems", Joint International Symposium on The Social Impacts of Developments in Information, Manufacturing and Service Systems, Istanbul, Turkey, pp. 260-269 (2014).

23. Da Costa Fontes, F.F. and Goncalves, G. "Routing problem with pendular and cyclic service in a hierarchical structure of hub and spoke with multiple allocation of sub-hubs", International Conference on Industrial Engineering and Systems Management, Seville, Spain, pp. 561-567 (2015). DOI: 10.1109/IESM.2015.7380214.

24. Mahmutogullari, A.I. and Kara, B.Y. "Hub location under competition", European Journal of Operational Research, 250(1), pp. 214-225 (2016). DOI: 10.1016/j.ejor.2015.09.008.

25. Kim, J., Lee, S., and Lee, S. "An evacuation route choice model based on multi-agent simulation in order to prepare Tsunami disasters", Transportmetrica B: Transport Dynamics, 5(4), pp. 385-401 (2017). DOI: 10.1080/21680566.2016.1147002.

26. Torkestani, S., Seyedhosseini, S.M., Makui, A., et al. "The reliable design of a hierarchical multi-modes transportation hub location problems (HMMTHLP) under dynamic network disruption (DND)", Computers & Industrial Engineering, 122, pp. 39-86 (2018). DOI: 10.1016/j.cie.2018.05.027.

27. Cohon, J.L., Multi-Objective Programming and Planning, Chapter 6.2, 2nd Edn., Dover Publications (2013).

28. Ernest, A.T. and Krishnamoorthy, M. "Efficient algorithms for the uncapacitated single allocation-hub median problem", Location Science, 4(3), pp. 139-54 (1996). DOI: 10.1016/S0966-8349(96)00011-3.

29. Schott, J.R. "Fault tolerant design using single and multicriteria genetic algorithm optimization", Master's Thesis, MIT University (1995).

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