Document Type : Research Paper

**Authors**

Department of Industrial Engineering K.N.Toosi University of Technology, Iran, Tehran

**Abstract**

The optimal locating of facilities has large effects on economic benefits, providing satisfactory service and levels of customer satisfaction. One of the new topics discussed in location problems is hub location and hub facilities are subject to unpredictable disruptions. This paper proposes a nonlinear integer model for reliable single allocation hub location problem that considers backup hub, alternative routes, and also uses fortification approach to improve the network reliability. Due to the NP hard nature of the model, we use genetic algorithm in order to solve the defined problem and the numerical results illustrate the applicability of the proposed model as well as the efficiency of solution procedure.

**Keywords**

**Main Subjects**

An, Y., Zhang, Y. & Zeng, B., 2015. The reliable hub-and-spoke design problem: Models and algorithms. *Transportation Research Part B: Methodological*, 77, pp.103-122

Asl-Najafi, J., Zahiri, B., Bozorgi-Amiri, A. & Taheri-Moghaddam, A., 2015. A dynamic closed-loop location-inventory problem under disruption risk. *Computers & Industrial Engineering*, 90, pp.414-428

Azizi, N., Chauhan, S., Salhi, S. & Vidyarthi, N., 2016. The impact of hub failure in hub-and-spoke networks: Mathematical formulations and solution techniques. *Computers & Operations Research*, 65, pp.174-188

Bashiri, M., & M. Rezanezhad. "A reliable multi-objective p-hub covering location problem considering of hubs capabilities." *International Journal of Engineering-Transactions B: Applications* 28.5 (2015): 717.

Cui, T., Ouyang, Y. & Shen, Z.J.M., 2010. Reliable facility location design under the risk of disruptions. *Operations Research*, 58(4-part-1), pp.998-1011.

Drezner, Z., 1987. Heuristic solution methods for two location problems with unreliable facilities. *Journal of the Operational Research Society*, 38(6), pp.509-514.

Eghbali, M., Abedzadeh, M. & Setak, M., 2014. Multi-objective reliable hub covering location considering customer convenience using NSGA-II. *International Journal of System Assurance Engineering and Management*, 5(3), pp.450-460

Jalali, S., Seifbarghy, M., Sadeghi, J. & Ahmadi, S., 2016. Optimizing a bi-objective reliable facility location problem with adapted stochastic measures using tuned-parameter multi-objective algorithms. *Knowledge-Based Systems*, 95, pp.45-57.

Kim, H. & O'Kelly, M.E., 2009. Reliable p‐Hub Location Problems in Telecommunication Networks. *Geographical Analysis*, 41(3), pp.283-306.

Li, Q., Zeng, B. & Savachkin, A., 2013. Reliable facility location design under disruptions. Computers & Operations Research, 40(4), pp.901-909

Liberatore, F., Scaparra, M.P. & Daskin, M.S., 2012. Hedging against disruptions with ripple effects in location analysis. *Omega*, 40(1), pp.21-30.

Losada, C., Scaparra, M.P. & O’Hanley, J.R., 2012. Optimizing system resilience: a facility protection model with recovery time. *European Journal of Operational Research*, 217(3), pp.519-530

Medal, Hugh R., Edward A. Pohl, & Manuel D. Rossetti. "A multi-objective integrated facility location-hardening model: Analyzing the pre-and post-disruption tradeoff." *European Journal of Operational Research* 237.1 (2014): 257-270.

Mohammadi, M., Jolai, F. & Tavakkoli-Moghaddam, R., 2013. Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm. *Applied Mathematical Modelling*, 37(24), pp.10053-10073

Mohammadi, M., Tavakkoli-Moghaddam, R., Siadat, A. & Dantan, J.Y., 2016. Design of a reliable logistics network with hub disruption under uncertainty. *Applied Mathematical Modelling*, 40(9), pp.5621-5642

Mohammadi, M., Tavakkoli-Moghaddam, R., Siadat, A. & Rahimi, Y., 2016a. A game-based meta-heuristic for a fuzzy bi-objective reliable hub location problem*. Engineering Applications of Artificial Intelli*gence, 50, pp.1-19

Mohammadi, Mehrdad, Payman Jula, & Reza Tavakkoli-Moghaddam. "Design of a reliable multi-modal multi-commodity model for hazardous materials transportation under uncertainty." *European Journal of Operational Research* 257.3 (2017): 792-809.

Parvaresh, F., Golpayegany, S.H., Husseini, S.M. & Karimi, B., 2013. Solving the p-hub median problem under intentional disruptions using simulated annealing. *Networks and Spatial Economics*, 13(4), pp.445-470.

Parvaresh, F., Husseini, S.M., Golpayegany, S.H. & Karimi, B., 2014. Hub network design problem in the presence of disruptions. *Journal of Intelligent Manufacturing*, 25(4), pp.755-774

Peng, P., Snyder, L.V., Lim, A. & Liu, Z., 2011. Reliable logistics networks design with facility disruptions. *Transportation Research Part B: Methodologica*l, 45(8), pp.1190-1211.

Sadeghi, M., Jolai, F., Tavakkoli-Moghaddam, R. & Rahimi, Y., 2015. A new stochastic approach for a reliable p-hub covering location problem. *Computers & Industrial Engineering*, 90, pp.371-380.

Snyder, L.V. & Daskin, M.S., 2005. Reliability models for facility location: the expected failure cost case. *Transportation Science*, 39(3), pp.400-416.

Zarandi, M.F., Davari, S. & Sisakht, S.H., 2012. The Q-coverage multiple allocation hub covering problem with mandatory dispersion*. Scientia Iranica*, 19(3), pp.902-911

Zhang, Y., Snyder, L.V., Qi, M. & Miao, L., 2016. A heterogeneous reliable location model with risk pooling under supply disruptions. *Transportation Research Part B*: Methodological, 83, pp.151-178.

Winter 2019

Pages 83-94

**Receive Date:**12 August 2018**Revise Date:**18 September 2018**Accept Date:**31 October 2018