Abstract
In this paper, we formulate the disaster preparedness and short-term response planning problem through a multistage stochastic optimization model. We assume that both the demands and the road capacities have known but continuous distributions, which implies an infinite number of scenarios for the problem. Then, we discretize these continuous distributions using different sampling techniques, and build scenario trees which contain a big number of scenarios. To cope with the computationally untractable multi-dimensional integrations, we estimate the expectations by their Sample Average Approximations. Under some assumptions, we solve the resulting problems through the Stochastic Dual Dynamic Programming algorithm. We numerically derive useful insights for the applications of the algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wassenhove, L.N.V.: Humanitarian aid logistics: supply chain management in high gear. J. Oper. Res. Soc. 57(5), 475–489 (2006)
Hedgpeth, D.: U.S. task force commander for Haitian relief says logistics remain stumbling block. Washington Post, 18 Jan 2010. http://www.washingtonpost.com/wp-dyn/content/article/2010/01/18/AR2010011804059.html. Accessed 13 Dec 2013
BBC News: Logistical nightmare hampers Haiti aid effort, 22 Jan 2010. http://www.news.bbc.co.uk/go/pr/fr/-/2/hi/americas/8460787.stm. Accessed 13 Dec 2013
Galindo, G., Batta, R.: Review of recent developments in OR/MS research in disaster operations management. Eur. J. Oper. Res. 230, 201–211 (2013)
Caunhye, A.M., Nie, X., Pokharel, S.: Optimization models in emergency logistics. Socio Econ. Plan. Sci. 46(1), 4–13 (2012)
Haghani, A., Oh, S.-C.: Formulation and solution of a multi-commodity, multi-modal network flow model for disaster relief operations. Transp. Res. Part A 30(3), 231–250 (1996)
Barbarosoğlu, G., Arda, Y.: A two-stage stochastic programming framework for transportation planning in disaster response. J. Oper. Res. Soc. 55, 43–53 (2004)
Chiu, Y-C., Zheng, H., Villalobos, J., Gautam, B.: Modeling no-notice mass evacuation using a dynamic traffic flow optimization model. IIE Trans. 39, 83–94 (2007)
Yi, W., Özdamar, L.: A dynamic logistics coordination model for evacuation and support in disaster response activities. Eur. J. Oper. Res. 179, 1177–1193 (2007)
Lodree, E.J., Taskin, S.: Supply chain planning for hurricane response with wind speed information updates. Comput. Oper. Res. 36, 2–15 (2009)
Balcik, B., Beamon, B.M., Smilowitz, K.: Last mile distribution in humanitarian relief. J. Intell. Transp. Syst. 12(2), 51–63 (2008)
Rawls, C.G., Turnquist, M.A.: Pre-positioning of emergency supplies for disaster response. Transp. Res. Part B 44, 521–534 (2010)
Rawls, C.G., Turnquist, M.A.: Pre-positioning and dynamic delivery planning for short-term response following a natural disaster. Socio Econ. Plan. Sci. 46(1), 46–54 (2012)
An, S., Cui, N., Li, X., Ouyang, Y.: Location planning for transit-based evacuation under the risk of disruptions. Transp. Res. Part B 54, 1–16 (2013)
Homem-de-Mello, T., de Matos, V.L., Finardi, E.C.: Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in the long-term hydrotermal scheduling. Energy Syst. 2, 1–31 (2011)
Fu, M.: Optimization for simulation: theory vs. practice. INFORMS J. Comput. 14(3), 192–215 (2002)
Shapiro, A., Dentcheva, D., Ruszczyński, A.: Lectures on Stochastic Programming: Modeling and Theory. SIAM, Philadelphia (2009)
Infanger, G., Morton, D.P.: Cut sharing for multistage stochastic linear programs with interstage dependency. Math. Program. 75, 241–256 (2006)
McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239–245 (1979)
Loh, W.: On Latin hypercube sampling. Ann. Stat. 24(5), 2058–2080 (1996)
Owen, A.B.: Monte Carlo variance of scrambled net quadrature. SIAM J. Numer. Anal. 34(5), 1884–1910 (1997)
Stein, M.L.: Large sample properties of simulations using Latin hypercube sampling. Technometrics 29, 143–151 (1987)
Pereira, M.V.F., Pinto, L.M.V.G.: Multi-stage stochastic optimization applied to energy planning. Math. Program. 52, 359–375 (1991)
Philpott, A.B., Guan, Z.: On the convergence of stochastic dual dynamic programming and related methods. Oper. Res. Lett. 36, 450–455 (2008)
Shapiro, A.: Analysis of stochastic dual dynamic programming method. Eur. J. Oper. Res. 209, 63–72 (2011)
Shapiro, A., Tekaya, W., da Costa, J.P., Soares, M.P.: Risk neutral and risk averse stochastic dual dynamic programming method. Eur. J. Oper. Res. 224(2), 375–391 (2013)
Hobeika, A.G., Kim, C.: Comparison of traffic assignments in evacuation modeling. IEEE Trans. Eng. Manage. 45, 192–198 (1998)
Donnell, E.T., Hines, S.C., Mahoney, K.M., Porter, R.J., McGee, H.: Speed concepts: informational guide. Technical Report No. FHWA-SA-10-001, U.S. Department of Transportation, Federal Highway Administration (2009)
Erdik, M., Sesetyan, K., Hancilar, U., Demircioglu, M.B.: Earthquake risk assessment of an urban area: Istanbul. Unpublished manuscript obtained through private communication from M. Erdik, Boğaziçi University Kandilli Observatory and Earthquake Research Center, Istanbul, Turkey (2011)
Unpublished data obtained through private communication from A. Ansal, Boğaziçi University Kandilli Observatory and Earthquake Research Center, Istanbul, Turkey
Turkish Statistical Institute: http://www.turkstat.gov.tr
Law, A.M.: Simulation Modeling and Analysis, 4th edn. McGraw-Hill, New York (2007)
Acknowledgements
The author thanks Atilla Ansal and Mustafa Erdik (Boğaziçi University Kandilli Observatory and Earthquake Research Center) for giving their data of the estimated number of buildings that will be damaged at various levels after an earthquake in Istanbul. This research has been financially supported by Galatasaray University Research Fund.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media New York
About this chapter
Cite this chapter
Angün, E. (2015). Stochastic Dual Dynamic Programming Solution of a Short-Term Disaster Management Problem. In: Dellino, G., Meloni, C. (eds) Uncertainty Management in Simulation-Optimization of Complex Systems. Operations Research/Computer Science Interfaces Series, vol 59. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7547-8_10
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7547-8_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7546-1
Online ISBN: 978-1-4899-7547-8
eBook Packages: Business and EconomicsBusiness and Management (R0)