All Title Author
Keywords Abstract

A Lexicographic Approach to Postdisaster Relief Logistics Planning Considering Fill Rates and Costs under Uncertainty

DOI: 10.1155/2014/939853

Full-Text   Cite this paper   Add to My Lib


Predicting the occurrences of earthquakes is difficult, but because they often bring huge catastrophes, it is necessary to launch relief logistics campaigns soon after they occur. This paper proposes a stochastic optimization model for post-disaster relief logistics to guide the strategic planning with respect to the locations of temporary facilities, the mobilization levels of relief supplies, and the deployment of transportation assets with uncertainty on demands. In addition, delivery plans for relief supplies and evacuation plans for critical population have been developed for each scenario. Two objectives are featured in the proposed model: maximizing the expected minimal fill rate of affected areas, where the mismatching distribution among correlated relief demands is penalized, and minimizing the expected total cost. An approximate lexicographic approach is here used to transform the bi-objective stochastic programming model into a sequence of single objective stochastic programming models, and scenario-decomposition-based heuristic algorithms are furthermore developed to solve these transformed models. The feasibility of the proposed bi-objective stochastic model has been demonstrated empirically, and the effectiveness of the developed solution algorithms has also been evaluated and compared to that of commercial mixed-integer optimization software. 1. Introduction Earthquakes are a special type of natural disaster that can result in huge catastrophes. The Great Sichuan Earthquake, which occurred on May 12, 2008, in Wenchuan County, Sichuan Province, China, was one such case. It had a recorded magnitude of 8.0 and imposed tremendous suffering on the local residents, causing over 69,000 deaths, 18,000 missing persons cases, 374,000 injuries, and huge loss of property. Although thousands of networked seismograph stations have been installed around the world and although these stations use powerful computers, it is still difficult to predict when and where an earthquake will strike. Therefore, an effective and necessary approach coping with an earthquake disaster is to plan and implement a disaster relief campaign that would reduce the damage right after the earthquake disaster takes place. Emergency logistics plays a vital role in disaster relief campaigns. However, the planning and implementation of relief logistics are challenging, especially when help is needed in mountainous areas, where the transportation infrastructure, such as roads, bridges and railway lines, can suffer severe damage after large earthquakes. The following three factors


[1]  J.-B. Sheu, “Challenges of emergency logistics management,” Transportation Research E, vol. 43, no. 6, pp. 655–659, 2007.
[2]  S. Qing, “Ten major sciences and technologies for disaster rescue work in earthquake,” Science & Technology Review, vol. 26, pp. 19–24, 2008.
[3]  B. Balcik and B. M. Beamon, “Facility location in humanitarian relief,” International Journal of Logistics Research and Applications, vol. 11, no. 2, pp. 101–121, 2008.
[4]  M.-S. Chang, Y.-L. Tseng, and J.-W. Chen, “A scenario planning approach for the flood emergency logistics preparation problem under uncertainty,” Transportation Research E, vol. 43, no. 6, pp. 737–754, 2007.
[5]  S. V. Ukkusuri and W. F. Yushimito, “Location routing approach for the humanitarian prepositioning problem,” Transportation Research Record, vol. 2089, pp. 18–25, 2008.
[6]  C. G. Rawls and M. A. Turnquist, “Pre-positioning of emergency supplies for disaster response,” Transportation Research B, vol. 44, no. 4, pp. 521–534, 2010.
[7]  C. G. Rawls and M. A. Turnquist, “Pre-positioning planning for emergency response with service quality constraints,” OR Spectrum, vol. 33, no. 3, pp. 481–498, 2011.
[8]  H. O. Mete and Z. B. Zabinsky, “Stochastic optimization of medical supply location and distribution in disaster management,” International Journal of Production Economics, vol. 126, no. 1, pp. 76–84, 2010.
[9]  J. Salmerón and A. Apte, “Stochastic optimization for natural disaster asset prepositioning,” Production and Operations Management, vol. 19, no. 5, pp. 561–574, 2010.
[10]  A. Bozorgi-Amiri, M. S. Jabalameli, and S. M. J. Mirzapour Al-e-Hashem, “A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty,” OR Spectrum, 2011.
[11]  A. D?yen, N. Aras, and G. Barbaroso?lu, “A two-echelon stochastic facility location model for humanitarian relief logistics,” Optimization Letters, vol. 6, no. 6, pp. 1123–1145, 2012.
[12]  J. R. Birge and F. Louveaux, Introduction to Stochastic Programming, Springer, New York, NY, USA, 1997.
[13]  C. C. Car?e and R. Schultz, “Dual decomposition in stochastic integer programming,” Operations Research Letters, vol. 24, no. 1-2, pp. 37–45, 1999.
[14]  G. Laporte and F. V. Louveaux, “The integer -shaped method for stochastic integer programs with complete recourse,” Operations Research Letters, vol. 13, no. 3, pp. 133–142, 1993.
[15]  S. Ahmed, M. Tawarmalani, and N. V. Sahinidis, “A finite branch-and-bound algorithm for two-stage stochastic integer programs,” Mathematical Programming A, vol. 100, no. 2, pp. 355–377, 2004.
[16]  H. D. Sherali and B. M. P. Fraticelli, “A modification of Benders' decomposition algorithm for discrete subproblems: an approach for stochastic programs with integer recourse,” Journal of Global Optimization, vol. 22, no. 1–4, pp. 319–342, 2002.
[17]  L. Ntaimo and S. Sen, “The million-variable “march” for stochastic combinatorial optimization,” Journal of Global Optimization, vol. 32, no. 3, pp. 385–400, 2005.
[18]  S. Sen and J. L. Higle, “The theorem and a algorithm for large scale stochastic mixed-integer programming: set convexification,” Mathematical Programming A, vol. 104, no. 1, pp. 1–20, 2005.
[19]  H. D. Sherali and X. Zhu, “On solving discrete two-stage stochastic programs having mixed-integer first- and second-stage variables,” Mathematical Programming B, vol. 108, no. 2-3, pp. 597–616, 2006.
[20]  S. Sen and H. D. Sherali, “Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming,” Mathematical Programming A, vol. 106, no. 2, pp. 203–223, 2006.
[21]  L. Li, M. Jin, and L. Zhang, “Sheltering network planning and management with a case in the Gulf Coast region,” International Journal of Production Economics, vol. 131, no. 2, pp. 431–440, 2011.
[22]  B. M. Beamon and B. Balcik, “Performance measurement in humanitarian relief chains,” International Journal of Public Sector Management, vol. 21, no. 1, pp. 4–25, 2008.
[23]  X. Prats, V. Puig, J. Quevedo, and F. Nejjari, “Multi-objective optimisation for aircraft departure trajectories minimising noise annoyance,” Transportation Research C, vol. 18, no. 6, pp. 975–989, 2010.
[24]  L. A. Wolsey, Integer Programming, John Wiley & Sons, New York, NY, USA, 1998.
[25]  A. Kokott and A. Lobel, “Lagrangian relaxations and subgradient methods for multiple-depot vehicle scheduling problems,” Working Paper, Konrad-Zuse-Zentrum fur Information stechnik Berlin, 1996.
[26]  F. Fumero, “A modified subgradient algorithm for Lagrangean relaxation,” Computers & Operations Research, vol. 28, no. 1, pp. 33–52, 2001.
[27]  National Disaster Reduction Commission of the P. R. China, Integrated Analysis and Assessment on Wenchuan Earthquake Disaster, Science Press, Beijing, China, 2008.
[28]  Y. Yuan, “Impact of intensity and loss assessment following the great Wenchuan Earthquake,” Earthquake Engineering and Engineering Vibration, vol. 7, no. 3, pp. 247–254, 2008.
[29]  L. ?zdamar, E. Ekinci, and B. Kü?ükyazici, “Emergency logistics planning in natural disasters,” Annals of Operations Research, vol. 129, pp. 217–245, 2004.
[30]  A. Haghani and S.-C. Oh, “Formulation and solution of a multi-commodity, multi-modal network flow model for disaster relief operations,” Transportation Research A, vol. 30, no. 3, pp. 231–250, 1996.


comments powered by Disqus