Abstract
Disaster responses are usually joint efforts between agencies of different sizes and specialties. Improving disaster response can be achieved by prepositioning relief items in the appropriate amount and at the appropriate locations. In this paper, we develop a multi-agency prepositioning model under uncertainty. In particular, we develop a model in which the prepositioning strategy developed by a major aid agency or a local government considers sharing resources with other aid agencies. The proposed model considers multiple relief item types, storage capacity, budgetary and equity constraints while integrating supplier selection, inventory and facility location decisions. Uncertainty is modeled using robust optimization. We provide a deterministic model as well as its robust counterpart where demand and link disruptions are considered uncertain. In addition, a heuristic approach for solving the uncapacitated deterministic version of the proposed model is provided. In order to evaluate the proposed model and heuristic, two computational experiments are presented. In the first experiment, we assess the quality of the robust solutions by simulating a number of realizations. In the second experiment, we test the performance of the heuristic compared to the optimal policy.
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References
Aharon B-T, Byung DC, Supreet RM, Tao Y (2011) Robust optimization for emergency logistics planning: risk mitigation in humanitarian relief supply chains. Transp Res Part B: Methodol 45(8):1177–1189
Akhtar P, Marr NE, Garnevska EV (2012) Coordination in humanitarian relief chains: chain coordinators. J Humanit Logist Supply Chain Manag 2(1):85–103
Akkihal A (2006) Inventory pre-positioning for humanitarian operations. PhD thesis, Massachusetts Institute of Technology
Ali B-A, Jabalameli MS, Mirzapour Al-e Hashem SMJ (2013) A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty. OR Spectr 35(4):905–933
Anurag V, Gaukler Gary M (2015) Pre-positioning disaster responsefacilities at safe locations: an evaluation of deterministic andstochastic modeling approaches. Comput Op Res 62:197–209
Apte A (2010) Humanitarian logistics: a new field of research and action, vol 7. Now Publishers Inc
Balcik B, Beamon Benita M (2008) Facility location in humanitarian relief. Int J Logist 11(2):101–121
Beamon Benita M, Kotleba Stephen A (2006) Inventory management support systems for emergency humanitarian relief operations in south sudan. Int J Logist Manag 17(2):187–212
Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton
Berkoune D, Renaud J, Rekik M, Ruiz A (2012) Transportation in disaster response operations. Soc-Econ Plan Sci 46(1):23–32
Bertsimas D, Sim M (2004) The price of robustness. Op Res 52(1):35–53
Burcu B, Beamon Benita M, Krejci Caroline C, Muramatsu Kyle M, Magaly R (2010) Coordination in humanitarian relief chains: practices, challenges and opportunities. Int J Prod Econ 126(1):22–34
Caunhye Aakil M, Xiaofeng N, Shaligram P (2012) Optimization models in emergency logistics: a literature review. Soc-Econ Plan Sci 46(1):4–13
Center for Research on the Epidemiology of Disasters (CRED). Annual disaster statistical review 2017, 2018. https://cred.be/sites/default/files/adsr_2017.pdf
Chang M-S, Tseng Y-L, Chen J-W (2007) A scenario planning approach for the flood emergency logistics preparation problem under uncertainty. Transp Res Part E: Logist Transp Rev 43(6):737–754
Dimitris B, Brown David B, Constantine C (2011) Theory and applications of robust optimization. SIAM Rev 53(3):464–501
Döyen A, Aras N, Barbarosoğlu G (2012) A two-echelon stochastic facility location model for humanitarian relief logistics. Optim Lett 6(6):1123–1145
Dunning IR (2016) Advances in robust and adaptive optimization: algorithms, software, and insights. PhD thesis, Massachusetts Institute of Technology
Feng C, Fan G , Zhang Y, Yang T (2010) Collaboration in humanitarian logistics. In: ICLEM 2010: Logistics for sustained economic development: infrastructure, information, integration, pp 1127–1133
Ferrer José M, Teresa Ortuño M, Gregorio T (2016) A grasp metaheuristic for humanitarian aid distribution. J Heuristics 22(1):55–87
Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: an overview. Eur J Op Res 235(3):471–483
Galindo G, Batta R (2013a) Prepositioning of supplies in preparation for a hurricane under potential destruction of prepositioned supplies. Soc-Econ Plan Sci 47(1):20–37
Galindo G, Batta R (2013b) Review of recent developments in or/ms research in disaster operations management. Eur J Op Res 230(2):201–211
Grass E, Fischer K (2016) Two-stage stochastic programming in disaster management: a literature survey. Surv Op Res Manag Sci 21:85–100
Gustavsson L (2003) Humanitarian logistics: context and challenges. Forced Migr Rev 18(6):6–8
International Federation of Red Cross and Red Crescent Societies (IFRC). World disasters report: Focus on local actor, the key to humanitarian effectiveness, (2015). http://ifrc-media.org/interactive/world-disasters-report-2015/
International Federation of Red Cross and Red Crescent Societies (IFRC). World disasters report: leaving no one behind, (2018). https://media.ifrc.org/ifrc/world-disaster-report-2018/
Kay MG (2013) Matlog: logistics engineering matlab toolbox. http://www4.ncsu.edu/~kay/matlog/
Kuehn Alfred A, Hamburger Michael J (1963) A heuristic program for locating warehouses. Manag Sci 9(4):643–666
Mert A, Adivar BO (2010) Fuzzy disaster relief planning with credibility measures. In: 24th Mini EURO conference on Continuous optimization and information-based technologies in the financial sector, June, pp 23–26
Michael C, Richard P, Gyöngyi K, Spens Karen M (2011) Trends and developments in humanitarian logistics-a gap analysis. Int J Phys Distrib Logist Manag 41(1):32–45
Nezih A, Green Walter G (2006) Or/ms research in disaster operations management. Eur J Op Res 175(1):475–493
Ni W, Shu J, Song M (2018) Location and emergency inventory pre-positioning for disaster response operations: min-max robust model and a case study of yushu earthquake. Prod Op Manag 27(1):160–183
Onur MH, Zabinsky Zelda B (2010) Stochastic optimization of medical supply location and distribution in disaster management. Int J Prod Econ 126(1):76–84
Peng P, Snyder Lawrence V, Andrew L, Zuli L (2011) Reliable logistics networks design with facility disruptions. Transp Res Part B: Methodol 45(8):1190–1211
Qian W, Rajan B, Joyendu B, Rump Christopher M (2003) Budget constrained location problem with opening and closing of facilities. Comput Op Res 30(13):2047–2069
Rawls Carmen G, Turnquist Mark A (2010) Pre-positioning of emergency supplies for disaster response. Transp Res Part B: Methodol 44(4):521–534
Rawls Carmen G, Turnquist Mark A (2012) Pre-positioning and dynamic delivery planning for short-term response following a natural disaster. Soc-Econ Plan Sci 46(1):46–54
Rezaei-Malek M, Tavakkoli-Moghaddam R (2014) Robust humanitarian relief logistics network planning. Uncertain Supply Chain Manag 2(2):73–96
Salmerón J, Apte A (2010) Stochastic optimization for natural disaster asset prepositioning. Prod Op Manag 19(5):561–574
Serhan D, Gutierrez Marco A, Pinar K (2011) Pre-positioning of emergency items for care international. Interfaces 41(3):223–237
Shiva Z, Ali B-A, Jafar SS (2016) A robust optimization model for humanitarian relief chain design under uncertainty. Appl Math Model 40(17):7996–8016
Soyster Allen L (1973) Technical noteconvex programming with set-inclusive constraints and applications to inexact linear programming. Op Res 21(5):1154–1157
Stefan R, Gutjahr Walter J (2014) A math-heuristic for the warehouse location-routing problem in disaster relief. Comput Op Res 42:25–39
Trevor H, Moberg Christopher R (2005) Improving supply chain disaster preparedness: a decision process for secure site location. Int J Phys Distrib Logist Manag 35(3):195–207
Van Wassenhove LN (2006) Humanitarian aid logistics: supply chain management in high gear. J Op Res Soc 57(5):475–489
Yi W, Özdamar L (2007) A dynamic logistics coordination model for evacuation and support in disaster response activities. Eur J Op Res 179(3):1177–1193
Acknowledgements
We would like to thank Dr. Julie Casani, former Director of Public Health Preparedness for the state of North Carolina and Adjunct Associate Professor of Biological Sciences at NC State University and Dr. Michael Kay, Associate Professor at NC State University, for their valuable suggestions.
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Velasquez, G.A., Mayorga, M.E. & Cruz, E.A.R. Prepositioning inventory for disasters: a robust and equitable model. OR Spectrum 41, 757–785 (2019). https://doi.org/10.1007/s00291-019-00554-z
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DOI: https://doi.org/10.1007/s00291-019-00554-z