A Robust Programming Approach to Bi-objective Optimization Model in the Disaster Relief Logistics Response Phase

Document Type : Research Paper


1 Birjand university of technology, Birjand, Iran

2 Iran University of Science and Technology, Tehran, Iran


Accidents and natural disasters and crises coming out of them indicate the importance of an integrated planning to reduce their effected. Therefore, disaster relief logistics is one of the main activities in disaster management. In this paper, we study the response phase of the disaster management cycle and a bi-objective model has been developed for relief chain logistic in uncertainty condition including uncertainty in traveling time an also amount of demand in damaged areas. The proposed mathematical model has two objective functions. The first one is to minimize the sum of arrival times to damaged area multiplying by amount of demand and the second objective function is to maximize the minimum ratio of satisfied demands in total period in order to fairness in the distribution of goods. In the proposed model, the problem has been considered periodically and in order to solve the mathematical model, Global Criterion method has been used and a case study has been done at South Khorasan.


Main Subjects

Barbarosoglu, G. and Arda, Y., (2004). A two-stage stochastic programming framework for transportation planning in disaster response, Journal of Operational Research. Society, Vol. 55, pp. 43–53.
Barbarosoglu, G., Ozdamar, L. and Cevik, A., (2002). An interactive approach for hierarchical analysis of helicopter logistics in disaster relief operations, Eur. J. Operation Res., Vol. 140, pp. 118–133.
Beltrami, E.J. and Bodin, L.D., (1974). Networks and vehicle routing for municipal waste collection, Networks, Vol. 4 (1), pp. 65-94.
Berkoune, D., Renaud, J.R., Rekik, M. and Ruiz A., (2012). Transportation in disaster response operations, Socio-Economic Planning Sciences, Vol. 46, pp.23-32.

Bozorgi-Amiri, A., Jabalameli, M. and Mirzapour Al-e-Hashem, S. (2013). A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty. OR Spectrum, Vil. 35, pp. 905–933.

Christofides, N., Beasley, J.E., (1984). The period routing problem, Networks, Vol.14(2), pp. 237–256.
Eshghi, K. and Najafi, M., (2013). A logistics planning model to improve the response phase of earthquake, International Journal of Industrial Engineering & Production Management, Vol. 23(4), pp. 401-416.
Ke, L. and Feng, Z., (2013). A two-phase metaheuristic for the cumulative capacitated vehicle routing problem, Computers & Operations Research, Vol. 40, pp. 633–638.

Knott, R., (1988). Vehicle routing for emergency relief management: a knowledge - based approach, Disaster, Vol. 12, pp. 285–293.

Lai, Y. and Hwang, C., (1992). A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, Vol. 49, pp. 121–133.

Lin, Y.H, Batta, R., Rogerson, A.P., Blatt, A. and Flanigan M., (2011). A logistics model for emergency supply of critical items in the aftermath of a disaster, Socio-Economic Planning Sciences, Vol. 45, pp.132-145.

Mohammad Rezaei-Malek M. and Tavakkoli-Moghaddam R., (2014). Robust humanitarian relief logistics network planning, Uncertain Supply Chain Management Vol. 2, pp. 73–96. Mulvey, J.M., Vanderbei, R.J. and Zenios, S.A. (1995). Robust optimization of large-scale systems. Operations Research, Vol. 43, pp. 264–281.

Najafi, M., Eshghi, K. and Dullaert, W. (2013). A multi-objective robust optimization model for logistics planning in the earthquake response phase. Transportation Research Part E: Logistic and Transportation Review, Vol. 49, pp. 217–249.

Nolz, P.C., Semet, F. and Doerner, K.F., (2011). Risk approaches for delivering disaster relief supplies, OR Spectrum, Vol. 33, pp. 543–569. Oh, S. and Haghani, A., (1996). Formulation and solution of a multi-Commodity, multi-modal network flow model for disaster relief operations, Transport. Res., Vol. 30, pp. 231–250.

Ozdamar, L., Ekinci, E. and Kucukyazici, B. (2004). Emergency logistics planning in natural disasters, Annals of Operations Research, Vol. 129, pp. 217–245.

Pishvaee, M.S. and Torabi, S.A., (2010). A possibilistic programming approach for closed-loop supply chain network design under uncertainty, Fuzzy Sets and Systems, Vol. 161(20), pp. 26682683.

Rath, S. and Gutjahr, W.J., (2014). A math-heuristic for the warehouse location–routing problem in disaster relief, Computers & Operations Research, Vol. 42, pp. 25-39. Rao, S.S. (1996). Engineering optimization: theory and practice. 3rd ed. John Wiley & Sons, New Jersey.

Thomas, A.S. and Kopczak L.R. (2005). From logistics to supply chain management: the path forward in the humanitarian sector. http://www.fritzinstitute.org/PDFs/WhitePaper/ FromLogisticsto.pdf. Accessed 10 Oct 2010.

Van Wassenhove, L.N. (2006). Humanitarian aid logistics: supply chain management in high gear, J Oper Res Soc, Vol. 57, pp. 475–489.
Van Wassenhove, L.N. and Pedraza Martinez, A.J. (2012). Using OR to adapt supply chain management best practices to humanitarian logistics, International Transactions in operational Research, Vol.19, pp. 307-322.
Ulrich, N.S., Prins, C. and Wolfler C.R., (2010). An effective memetic algorithm for the cumulative capacitated vehicle routing problem, Computers & Operations Research, Vol. 37, pp. 1877-1885.
Zeleny M. (1982). Multiple Criteria Decision Making, MCGraw-Hill, New York.
Zhang, Z.-H. and Jiang, H. (2014). A robust counterpart approach to the bi-objective emergency medical service design problem. Applied Mathematical Modeling, Vol. 38, pp. 1033-1040.