A stochastic mathematical model to locate field hospitals under disruption uncertainty for large-scale disaster preparedness

Nezir Aydin


In this study, we consider field hospital location decisions for emergency treatment points in response to large scale disasters. Specifically, we developed a two-stage stochastic model that determines the number and locations of field hospitals and the allocation of injured victims to these field hospitals. Our model considers the locations as well as the failings of the existing public hospitals while deciding on the location of field hospitals that are anticipated to be opened. The model that we developed is a variant of the P-median location model and it integrates capacity restrictions both on field hospitals that are planned to be opened and the disruptions that occur in existing public hospitals. We conducted experiments to demonstrate how the proposed model can be utilized in practice in a real life problem case scenario. Results show the effects of the failings of existing hospitals, the level of failure probability and the capacity of projected field hospitals to deal with the assessment of any given emergency treatment system’s performance. Crucially, it also specifically provides an assessment on the average distance within which a victim needs to be transferred in order to be treated properly and then from this assessment, the proportion of total satisfied demand is then calculated.


Stochastic programming; humanitarian logistics; reliable facility location; field hospital; Istanbul.

Full Text:



Balcik, B., and Beamon B.M., Facility location in humanitarian relief. International Journal of Logistics, 11(2): 101-121 (2008). Crossref

Paul JA, Hariharan G. Location-Allocation Planning of Strategic Stockpile Locations for Effective Disaster Mitigation. Annals of Operations Research 196(1): 469-490 (2012). Crossref

Pengfei, Y., Santhosh K.G., Jomon A.P., and Lin L. Hospital capacity planning for disaster emergency management. Socio-Economic Planning Sciences. 44(3): 151-160 (2010). Crossref

Sheffi, Y. The resilient enterprise: overcoming vulnerability for competitive ad¬vantage. MIT Press Books. 1 (2003).

Pinto, C. M., Lopes, A. M., and Machado, J. T. Casualties Distribution in Human and Natural Hazards. In Mathematical Methods in Engineering (pp. 173-180). Springer Netherlands (2014). Crossref

Unesco. Learning from the great east japan earthquake and tsunami policy perspectives. Available from: http://www.unesco.org/new/en/media-services/singleview/news/learning_from_the_great_east_japan_earthquake_and_tsunami_policy_perspectives/. Accessed 4 March 2015.

Kreiss, Y., Merin, O., Peleg, K., Levy, G., Vinker, S., Sagi, R., Abargel, A., et al. Early disaster response in Haiti: the Israeli field hospital experience. Annals of Internal Medicine. 153 (1): 45-48 (2010). Crossref

Kaji, A.H., Koeing, K.L., and Lewis, R.J. Current hospital disaster preparedness. Jama: The Journal Of The American Medical Association. 298 (18): 2188-2190 (2007). Crossref

Rubinson, L., Nuzzo, J.B., Talmor, D.S., O'Toole, T., Kramer, B.R., and Inglesby, T.V. Augmentation of hospital critical care capacity after bioterrorist attacks or epidemics: Recommendations of the Working Group on Emergency Mass Critical Care++. Critical Care Medicine. 33(10): E2393 (2005). Crossref

Kanter, R.K., and Moran J.R. Pediatric hospital and intensive care unit capacity in regional disasters: expanding capacity by altering standards of care. Pediatrics. 119(1): 94-100 (2007). Crossref

Murali, P., Ordó-ez, F., and Dessouky, M.M. Facility location under demand uncertainty: Response to a large-scale bio-terror attack. Socio-Economic Planning Sciences. 46(1): 78-87 (2012). Crossref

Bar-Dayan, Y., et al., A multidisciplinary field hospital as a substitute for medical hospital care in the aftermath of an earthquake: the experience of the Israeli Defense Forces Field Hospital in Duzce, Turkey. Prehospital and Disaster Medicine. 20 (2): 103-106 (1999). Crossref

Bar-Dayan, Y., et al., An earthquake disaster in Turkey: an overview of the experience of the Israeli Defence Forces Field Hospital in Adapazari. Disasters. 24(3): 262-270 (2000). Crossref

Berman, O., and Gavious, A. Location of terror response facilities: A game between state and terrorist. European Journal of Operational Research, 177(2), 1113-1133 (2007). Crossref

Paul, J.A., and Batta, R. Models for hospital location and capacity allocation for an area prone to natural disasters. International Journal of Operational Research. 3(5): 473-496 (2008). Crossref

Salmerón, J., and Apte, A. Stochastic optimization for natural disaster asset prepositioning. Production and Operations Management, 19(5), 561-574 (2010). Crossref

Campbell, A. M., and Jones, P. C. Prepositioning supplies in preparation for disasters. European Journal of Operational Research, 209(2), 156-165 (2011). Crossref

Galindo, G., and Batta, R. Prepositioning of supplies in preparation for a hurricane under potential destruction of prepositioned supplies. Socio-Economic Planning Sciences, 47(1), 20-37 (2013). Crossref

Kaji, A.H., and Lewis, R.J. Hospital disaster preparedness in Los Angeles county. Academic Emergency Medicine. 13(11): 1198-1203 (2006). Crossref

Paul, J.A., and Hariharan, G. Hospital capacity planning for efficient disaster mitigation during a bioterrorist attack. In Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come. IEEE Press.:1139-1147 (2007).

Altay, N., and Green-III, W.G., OR/MS research in disaster operations management. European Journal of Operational Research. 175(1): 475-493 (2006). Crossref

Gormez, N.,. Disaster response and relief facility location for Istanbul. PhD dissertation. Middle East Technical University (2008).

Wright, P.D., Liberatore, M.J., and Nydick, R.L. A survey of operations research models and applications in homeland security. Interfaces. 36(6): 514-529 (2006). Crossref

Dekle, J., Lavieri, M.S., Martin, E., Emir-Farinas, H., and Francis, R.L., A Florida county locates disaster recovery centers. Interfaces. 35(2): 133-139 (2005). Crossref

Jia, H., Ordó-ez, F., and Dessouky, M., A modeling framework for facility location of medical services for large-scale emergencies. IIE Transactions. 39(1): 41-55 (2007). Crossref

Gunnec, D., and Salman, F., A two-stage multi-criteria stochastic programming model for location of emergency response and distribution centers. International Network Optimization Conference (2007).

Tzeng, G-H., Cheng, H-J., and Huang, T.D. Multi-objective optimal planning for designing relief delivery systems. Transportation Research Part E: Logistics and Transportation Review. 43(6): 673-686 (2007). Crossref

Serra, D., and Marianov., V. The p-median problem in a changing network: the case of Barcelona. Location Science. 6(1):383-394 (1998). Crossref

Barbarosoğlu, G., and Arda, Y., A two-stage stochastic programming framework for transportation planning in disaster response. Journal of the Operational Research Society 55(1): 43-53 (2004). Crossref

Drezner, Z., and Hamacher, H.W.Eds., Facility location: applications and theory. Springer. Verlag (2004).

Church, R., and Velle, C.R., The maximal covering location problem. Papers in Regional Science. 32(1): 101-118 (1974). Crossref

Berman, O., Drezner, Z., and Wesolowsky, G.O., Locating service facilities whose reliability is distance dependent. Computers & Operations Research. 30(11): 1683-1695 (2003). Crossref

Batta, R., Larson, R.C., and Odoni, A.R., A single‐server priority queueing location model. Networks.18(2): 87-103 (1988). Crossref

Aydin, N., and Murat, A., A swarm intelligence based sample average approximation algorithm for the capacitated reliable facility location problem. International Journal of Production Economics. 145(1):173-183 (2012). Crossref

Schütz, P., Tomasgard, A., and Ahmed, S. Supply chain design under uncertainty using sample average approximation and dual decomposition. European Journal of Operational Research. 199(2): 409-419 (2009). Crossref

Masihtehrani, B., Stochastic analysis of disruption in supply chain networks. PhD dissertation. The Pennsylvania State University, (2011).

Snyder, L.V., Scaparra, M.P., Daskin, M.S., and Church, R.L. Planning for disruptions in supply chain networks. Tutorials In Operations Research (2006). Crossref

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

Shen, Z.J.M., Zhan, R.L., and Zhang, J. "The reliable facility location problem: Formulations, heuristics, and approximation algorithms. INFORMS Journal on Computing. 23(3): 470-482 (2011). Crossref

Snyder, L.V., and Ülker, N.Ş. A model for locating capacitated, unreliable facilities. In IERC Conference, Atlanta, GA (2005).

Gade, D., Capacitated facilities location problems with unreliable facilities. ProQuest (2007).

JICA. The study on a disaster prevention / mitigation basic plan in Istanbul including seismic micronization in the republic of Turkey. Final report, Japan International Cooperation Agency (2002).

Gormez, N., Koksalan, M., and Salman, F.S., Locating disaster response facilities in Istanbul. Journal of the Operational Research Society. 62(7): 1239-1252 (2010). Crossref

Saglik (2015). Available from: http://www.saglik.gov.tr/EN/ana-sayfa/2-0/20130617.html. Accessed 20 September 2015.

Meb. (2015). Available from: http://www.meb.gov.tr/english/indexeng.html. Accessed 12 December 2015.

Zeytinburnu (2015). Available from: http://www.zeytinburnu.bel.tr/Page/376/ news/news-from-municipal.aspx. Accessed 17 August 2015.

Google (2015). Available from: http://maps.google.com/. Accessed 24 December 2015.

Tuik (2015). Available from: http://www.tuik.gov.tr/AltKategori.do?ust_id=11. Accessed 18 October 2015.

Ayvaz, B., Bolat, B., and Aydin, N. (2015). Stochastic reverse logistics network design for waste of electrical and electronic equipment. Resources, Conservation and Recycling, 104, 391-404. Crossref

DOI: http://dx.doi.org/10.11121/ijocta.01.2016.00296


  • There are currently no refbacks.

Copyright (c) 2016 Nezir Aydin

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


   ithe_170     crossref_284         ind_131_43_x_117_117  Scopus  EBSCO_Host    ULAKBIM     ZBMATH more...