Abstract
We develop a two-stage stochastic programming model for a humanitarian relief logistics problem where decisions are made for pre- and post-disaster rescue centers, the amount of relief items to be stocked at the pre-disaster rescue centers, the amount of relief item flows at each echelon, and the amount of relief item shortage. The objective is to minimize the total cost of facility location, inventory holding, transportation and shortage. The deterministic equivalent of the model is formulated as a mixed-integer linear programming model and solved by a heuristic method based on Lagrangean relaxation. Results on randomly generated test instances show that the proposed solution method exhibits good performance up to 25 scenarios. We also validate our model by calculating the value of the stochastic solution and the expected value of perfect information.
Similar content being viewed by others
References
Ahmed S., Tawarmalani M., Sahinidis N.V.: A finite branch-and-bound algorithm for two stage stochastic integer programming. Math. Progr. Ser. A B 100(2), 355–377 (2004)
Alonso-Ayuso A., Escudero L.F., Garín A., Ortuño M.T., Pérez G.: An Approach for strategic supply chain planning under uncertainty based on stochastic 0-1 programming. J. Glob. Optim. 26(1), 97–124 (2003)
Balcik B., Beamon B.M.: Facility location in humanitarian relief. Int. J. Logist. Res. Appl. 11(2), 101–121 (2008)
Beamon B.M., Balcik B.: Performance measurement in humanitarian relief chains. Int. J. Public Sect. Manag. 21, 4–25 (2008)
Bibbee, A., Gonenc, R., Jacobs, S., Konvitz, J., Price, R.: Economic effects of the 1999 Turkish earthquakes: an interim report. Organization for Economic Co-operation and Development (OECD) Economics Department Report (2000)
Birge J.R., Louveaux F.: Introduction to Stochastic Programming. Springer, New York (1997)
Caroe C.C., Schultz R.: Dual decomposition in stochastic integer programming. Oper. Res. Lett. 24, 37–45 (1999)
Caroe C.C., Tind J.: L-Shaped decomposition of two-stage stochastic programs with integer recourse. Math. Progr. 83, 451–464 (1998)
Carson Y., Batta R.: Locating an ambulance on the Amherst campus of the State University of New York at Buffalo. Interfaces 20, 43–49 (1990)
Chang M.S., Tseng Y.L., Chen J.W.: A scenario planning approach for the flood emergency logistics preparation problem under uncertainty. Transp. Res. Part E 43, 737–754 (2007)
Duran, S., Gutierrez, M.A., Keskinocak, P.: Pre-positioning of emergency items worldwide for CARE international. Interfaces 41(3) (2011)
Eaton D.J., Sanchez H.M., Lantigua R.R., Morgan J.: Determining ambulance deployment in Santo Domingo, Dominican Republic. J. Oper. Res. Soc. 37, 113–126 (1986)
Held M., Wolfe P., Crowder H.: Validation of subgradient optimization. Math. Progr. 6, 62–88 (1974)
Görmez N., Köksalan M., Salman F.S.: Locating disaster response facilities in Istanbul. J. Oper. Res. Soc. 62(7), 1239–1252 (2011)
Günneç, D., Salman, F.S.,: A two stage multi-criteria stochastic programming model for location of emergency response and distribution centers, vol. 35. Euro Winter Institute on Location and Logistics, Estoril, Portugal, pp. 209–227
Hogan K., ReVelle C.: Concepts and applications of backup coverage. Manag. Sci. 32, 1434–1444 (1986)
IBM (ILOG User Manual for CPLEX version 11.1) (2008)
Jayaraman V., Pirkul H.: Planning and coordination of production and distribution facilities for multiple commodities. Eur. J. Oper. Res. 133, 394–408 (2001)
Jia H., Ordonez F., Dessouky M.M.: A modeling framework for facility location of medical services for large-scale emergencies. IIE Trans. 39, 41–55 (2007)
Jia H., Ordonez F., Dessouky M.M.: Solution approaches for facility location of medical supplies for large-scale emergencies. Comput. Ind. Eng. 52, 257–276 (2007)
Karaman H., Şahin M., Elnashai A.S., Pineda O.: Loss assessment study for the Zeytinburnu district of İstanbul using Maeviz-Istanbul (HAZTURK). J. Earthq. Eng. 12(1), 187–198 (2008)
Klein Haneveld W.K., Vander Vlerk M.H.: Stochastic integer programming: general models and algorithms. Ann. Oper. Res. 85, 39–57 (1999)
Klein Haneveld W.K., Vander Vlerk M.H.: Optimizing electricity distribution using two-stage integer recourse models. In: Uryasev, S., Pardalos, P.M. (eds) Stochastic Optimization: Algorithms and Applications, pp. 137–154. Kluwer, Dordrecht (2001)
Laporte G., Louveaux F.V.: The integer L-shaped method for stochastic integer programs with complete recourse. Oper. Res. Lett. 13, 133–142 (1993)
Li L., Jin M., Zhang L.: Sheltering network planning and management with a case in the Gulf Coast region. Int. J. Prod. Econ. 131, 431–440 (2011)
Martello S., Toth P.: An algorithm for the generalized assignment problem. In: Brans, J.P. (eds) Operational Research, IFORS, pp. 589–603. North-Holland, Amsterdam (1981)
Mete H.O., Zabinsky Z.B.: Stochastic optimization of medical supply location and distribution in disaster management. Int. J. Prod. Econ. 126(1), 76–84 (2010)
Noyan N.: Risk-averse two-stage stochastic programming with an application to disaster management. Comput. Oper. Res. 39, 541–559 (2012)
Ntaimo L., Tanner M.W.: Computations with disjunctive cuts for two-stage stochastic mixed 0-1 integer programs. J. Glob. Optim. 41(3), 365–384 (2008)
Pardalos, P.M., Du, D.: Network Design: Connectivity and Facilities Location. DIMACS Series, vol. 40. American Mathematical Society (1998)
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 planning for emergency response with service quality constraints. OR Spectr. 33, 481–498 (2011)
Schilling D., Elzinga D., Cohon J., Church R., ReVelle C.: The TEAM/FLEET models for simultaneous facility and equipment siting. Transp. Sci. 13, 163–175 (1979)
Schilling D.A.: Strategic facility planning: the analysis of options. Decis. Sci. 13, 1–14 (1982)
Schultz R., Stougie L., van der Vlerk M.H.: Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis reductions. Math. Progr. 83, 229–252 (1998)
Schultz R., Tiedemann S.: Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse. SIAM J. Optim. 14, 115–138 (2003)
Schultz R.: Stochastic programming with integer variables. Math. Progr. 97(1), 285–309 (2003)
Serra D., Marianov V.: The p-median problem in a changing network: the case of Barcelona. Locat. Sci. 6(4), 383–394 (1999)
Sherali H.D., Fraticelli B.M.P.: A modification of Benders’ decomposition algorithm for discrete subproblems: An approach for stochastic programs with integer recourse. J. Glob. Optim. 22(1–4), 319–342 (2002)
Snyder L.V.: Facility location under uncertainty: a review. IIE Trans. 38(7), 547–564 (2006)
Stougie L., Vander Vlerk M.H. et al.: Stochastic integer programming. In: Dell’Amico, M. (eds) Annotated Bibliographies in Combinatorial Optimization, pp. 127–141. Wiley, New York (1997)
Şengezer B., Ansal A.: Probabilistic evaluation of observed earthquake damage data in Turkey. Nat. Hazards 40, 305–326 (2007)
Tragantalerngsak S., Holt J., Ronnqvist M.: Lagrangian heuristics for the two-echelon, single source, capacitated facility location problem. Eur. J. Oper. Res. 102, 611–625 (1997)
Tragantalerngsak S., Holt J., Ronnqvist M.: An exact method for the two-echelon, single-source, capacitated facility location. Eur. J. Oper. Res. 12, 473–489 (2000)
Tzeng G.-H., Cheng H.-J., Huang T.D.: Multi-objective optimal planning for designing relief delivery systems. Transp. Res. Part E 43, 673–686 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Döyen, A., Aras, N. & Barbarosoğlu, G. A two-echelon stochastic facility location model for humanitarian relief logistics. Optim Lett 6, 1123–1145 (2012). https://doi.org/10.1007/s11590-011-0421-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-011-0421-0