A Robust Optimization Methodology for Multi-objective Location-transportation Problem in Disaster Response Phase under Uncertainty


1 Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran, Iran

2 Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran


This paper presents a multi-objective model for location-transportation problem under uncertainty that has been developed to respond to crisis. In the proposed model, humanitarian aid distribution centers (HADC), the number and location of them, the amount of relief goods stored in distribution centers, the amount of relief goods sent to the disaster zone, the number of injured people transferred to medical centers and the delivery of relief regarding the limits of capacity for transport, distribution centers and also available time and budget limits are all considered. This work aims at minimizing unfulfilled needs; that is meaning the number of people have not been transferred to medical centers. In order to take the inevitable uncertainty in some parameters into account, the primal deterministic model has been reformulated by applying the robust optimization approach. Also the performance of the both deterministic and robust models are investigated by solving a numerical example. The results of the study show that the robust counterpart of deterministic model will remain feasible with a high probability in reality.  


1.     Altay, N. and Green III, W.G., "Or/ms research in disaster operations management", European Journal of Operational Research,  Vol. 175, No. 1, (2006), 475-493.
2.     Abounacer, R., Rekik, M. and Renaud, J., "An exact solution approach for multi-objective location–transportation problem for disaster response", Computers & Operations Research,  Vol. 41, (2014), 83-93.
3.     Vitoriano, B., Ortuño, M.T., Tirado, G. and Montero, J., "A multi-criteria optimization model for humanitarian aid distribution", Journal of Global Optimization,  Vol. 51, No. 2, (2011), 189-208.
4.     Najafi, M., Eshghi, K. and Dullaert, W., "A multi-objective robust optimization model for logistics planning in the earthquake response phase", Transportation Research Part E: Logistics and Transportation Review,  Vol. 49, No. 1, (2013), 217-249.
5.     Moreno, A., Alem, D. and Ferreira, D., "Heuristic approaches for the multiperiod location-transportation problem with reuse of vehicles in emergency logistics", Computers & Operations Research,  Vol. 69,  (2016), 79-96.
6.     Rodríguez-Espíndola, O., Albores, P. and Brewster, C., "Disaster preparedness in humanitarian logistics: A collaborative approach for resource management in floods", European Journal of Operational Research,  Vol. 264, No. 3, (2018), 978-993.
7.     Hasanzadeh, H. and Bashiri, M., "An efficient network for disaster management: Model and solution", Applied Mathematical Modelling,  Vol. 40, No. 5-6, (2016), 3688-3702.
8.     Duhamel, C., Santos, A.C., Brasil, D., Châtelet, E. and Birregah, B., "Connecting a population dynamic model with a multi-period location-allocation problem for post-disaster relief operations", Annals of Operations Research,  Vol. 247, No. 2, (2016), 693-713.
9.     Ruan, J., Wang, X., Chan, F. and Shi, Y., "Optimizing the intermodal transportation of emergency medical supplies using balanced fuzzy clustering", International Journal of Production Research,  Vol. 54, No. 14, (2016), 4368-4386.
10.   Fard, A.M.F. and Hajaghaei-Keshteli, M., "A tri-level location-allocation model for forward/reverse supply chain", Applied Soft Computing,  Vol. 62, (2018), 328-346.
11.   Singhtaun, C., "An exact algorithm for location–transportation problems in humanitarian relief", World Academy of Science, Engineering and Technology, International Journal of Social, Behavioral, Educational, Economic, Business and Industrial Engineering,  Vol. 9, No. 3, (2015), 815-819.
12.   Huang, K., Jiang, Y., Yuan, Y. and Zhao, L., "Modeling multiple humanitarian objectives in emergency response to large-scale disasters", Transportation Research Part E: Logistics and Transportation Review,  Vol. 75, (2015), 1-17.
13.   Wang, H., Du, L. and Ma, S., "Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake", Transportation Research Part E: Logistics and Transportation Review,  Vol. 69, (2014), 160-179.
14.   Ben-Tal, A., Do Chung, B., Mandala, S.R. and Yao, T., "Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains", Transportation Research part B: Methodological,  Vol. 45, No. 8, (2011), 1177-1189.
15.   Mete, H.O. and Zabinsky, Z.B., "Stochastic optimization of medical supply location and distribution in disaster management", International Journal of Production Economics,  Vol. 126, No. 1, (2010), 76-84.
16.   Berkoune, D., Renaud, J., Rekik, M. and Ruiz, A., "Transportation in disaster response operations", Socio-Economic Planning Sciences,  Vol. 46, No. 1, (2012), 23-32.
17.   Bozorgi-Amiri, A., Jabalameli, M. and Al-e-Hashem, S.M., "A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty", OR Spectrum,  Vol. 35, No. 4, (2013), 905-933.
18.   Rezaei, H., Zare, H.K., Bashiri, M. and Fakhrzad, M., "Re-configuration of the relief network considering uncertain demand and link failure in an earthquake: A multi-stage stochastic programming", International Journal of Engineering-Transactions C: Aspects,  Vol. 31, No. 6, (2018), 932-942.
19.   Bertsimas, D. and Sim, M., "The price of robustness", Operations research,  Vol. 52, No. 1, (2004), 35-53.
20.   Cheraghalipour, A., Paydar, M. and Hajiaghaei-Keshteli, M., "An integrated approach for collection center selection in reverse logistics", International Journal of Engineering-Transactions A: Basics,  Vol. 30, No. 7, (2017), 1005-1016.
21.   Nasiri, E., Afshari, A. and Hajiaghaei-Keshteli, M., "Addressing the freight consolidation and containerization problem by recent and hybridized meta-heuristic algorithms", International Journal of Engineering-Transactions C: Aspects,  Vol. 30, No. 3, (2017), 403-410.
22.   Rastaghi, M.M., Barzinpour, F. and Pishvaee, M., "A multi-objective hierarchical location-allocation model for the healthcare network design considering a referral system", International Journal of Engineering-Transactions B: Applications,  Vol. 31, No. 2, (2017), 365-373.