Markov Chain–Based Policies for Multistage Stochastic Integer Linear Programming with an Application to Disaster Relief Logistics

References

• Ahmed S, Cabral FG, Freitas Paulo da Costa B (2022) Stochastic Lipschitz dynamic programming. Math. Programming 191(2):755–793.Crossref, Google Scholar
• Alem D, Clark A, Moreno A (2016) Stochastic network models for logistics planning in disaster relief. Eur. J. Oper. Res. 255(1):187–206.Crossref, Google Scholar
• Bampou D, Kuhn D (2011) Scenario-free stochastic programming with polynomial decision rules. Proc. 50th IEEE Conf. Decision Control Eur. Control Conf. (IEEE, Piscataway, NJ), 7806–7812.Google Scholar
• Basciftci B, Ahmed S, Gebraeel N (2024) Adaptive two-stage stochastic programming with an analysis on capacity expansion planning problem. Manufacturing Service Oper. Management 26(6):2121–2141.Link, Google Scholar
• Bhattarai S, Song Y (2024) Multistage stochastic programming for integrated network optimization in hurricane relief logistics and evacuation planning. Networks 85(1):3–37.Crossref, Google Scholar
• Birge JR (1985) Decomposition and partitioning methods for multistage stochastic linear programs. Oper. Res. 33(5):989–1007.Link, Google Scholar
• Bodur M, Luedtke JR (2022) Two-stage linear decision rules for multi-stage stochastic programming. Math. Programming 191(1):347–380.Crossref, Google Scholar
• Bonnans JF, Cen Z, Christel T (2012) Energy contracts management by stochastic programming techniques. Ann. Oper. Res. 200(1):199–222.Crossref, Google Scholar
• Chen X, Sim M, Sun P, Zhang J (2008) A linear decision-based approximation approach to stochastic programming. Oper. Res. 56(2):344–357.Link, Google Scholar
• Davis LB, Samanlioglu F, Qu X, Root S (2013) Inventory planning and coordination in disaster relief efforts. Internat. J. Production Econom. 141(2):561–573.Crossref, Google Scholar
• Dowson O (2020) The policy graph decomposition of multistage stochastic programming problems. Networks 76(1):3–23.Crossref, Google Scholar
• Dowson O, Kapelevich L (2021) SDDP.jl: A Julia package for stochastic dual dynamic programming. INFORMS J. Comput. 33(1):27–33.Link, Google Scholar
• Duran S, Gutierrez MA, Keskinocak P (2011) Pre-positioning of emergency items for care international. Interfaces (Providence) 41(3):223–237.Link, Google Scholar
• Federal Emergency Management Agency (FEMA) (2021) National response framework. Accessed December 17, 2025, https://www.fema.gov/emergency-managers/national-preparedness/frameworks/response.Google Scholar
• Füllner C, Rebennack S (2025) Stochastic dual dynamic programming and its variants: A review. SIAM Rev. 67(3):415–539, Google Scholar
• Füllner C, Rebennack S (2022) Non-convex nested Benders decomposition. Math. Programming 1–38.Google Scholar
• Graumann A, Houston TG, Lawrimore JH, Levinson DH, Lott N, McCown S, Stephens S, et al. (2006) Hurricane Katrina: A climatological perspective: Preliminary report. Technical Report 2005-01, NOAA’s National Climatic Data Center, Washington, DC.Google Scholar
• Hjelmeland MN, Zou J, Helseth A, Ahmed S (2018) Nonconvex medium-term hydropower scheduling by stochastic dual dynamic integer programming. IEEE Trans. Sustainable Energy 10(1):481–490.Crossref, Google Scholar
• Holguín-Veras J, Pérez N, Jaller M, Van Wassenhove LN, Aros-Vera F (2013) On the appropriate objective function for post-disaster humanitarian logistics models. J. Oper. Management 31(5):262–280.Crossref, Google Scholar
• Kuhn D, Wiesemann W, Georghiou A (2011) Primal and dual linear decision rules in stochastic and robust optimization. Math. Programming 130(1):177–209.Crossref, Google Scholar
• Lodree EJ Jr, Ballard KN, Song CH (2012) Pre-positioning hurricane supplies in a commercial supply chain. Socio-Econom. Planning Sci. 46(4):291–305.Crossref, Google Scholar
• Löhndorf N, Shapiro A (2019) Modeling time-dependent randomness in stochastic dual dynamic programming. Eur. J. Oper. Res. 273(2):650–661.Crossref, Google Scholar
• Moreno A, Alem D, Ferreira D, Clark A (2018) An effective two-stage stochastic multi-trip location-transportation model with social concerns in relief supply chains. Eur. J. Oper. Res. 269(3):1050–1071.Crossref, Google Scholar
• Morton DP (1996) An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling. Ann. Oper. Res. 64(1):211–235.Crossref, Google Scholar
• Pacheco GG, Batta R (2016) Forecast-driven model for prepositioning supplies in preparation for a foreseen hurricane. J. Oper. Res. Soc. 67(1):98–113.Crossref, Google Scholar
• Pereira MV, Pinto LM (1991) Multi-stage stochastic optimization applied to energy planning. Math. Programming 52(1):359–375.Crossref, Google Scholar
• Pérez-Rodríguez N, Holguín-Veras J (2016) Inventory-allocation distribution models for postdisaster humanitarian logistics with explicit consideration of deprivation costs. Transportation Sci. 50(4):1261–1285.Link, Google Scholar
• Pernett SF, Amaya J, Arellana J, Cantillo V (2022) Questioning the implication of the utility-maximization assumption for the estimation of deprivation cost functions after disasters. Internat. J. Production Econom. 247:108435.Crossref, Google Scholar
• Philpott AB, De Matos VL (2012) Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion. Eur. J. Oper. Res. 218(2):470–483.Crossref, Google Scholar
• Philpott AB, Guan Z (2008) On the convergence of stochastic dual dynamic programming and related methods. Oper. Res. Lett. 36(4):450–455.Crossref, Google Scholar
• Regnier ED, MacKenzie CA (2019) The hurricane decision simulator: A tool for marine forces in new orleans to practice operations management in advance of a hurricane. Manufacturing Service Oper. Management 21(1):103–120.Link, Google Scholar
• Rivera-Royero D, Galindo G, Yie-Pinedo R (2016) A dynamic model for disaster response considering prioritized demand points. Socio-Econom. Planning Sci. 55:59–75.Crossref, Google Scholar
• Sabbaghtorkan M, Batta R, He Q (2020) Prepositioning of assets and supplies in disaster operations management: Review and research gap identification. Eur. J. Oper. Res. 284(1):1–19.Crossref, Google Scholar
• SCEMD (2023) Attachment a logistics plan to the South Carolina emergency operations plan. Accessed June 1, 2024, https://www.scemd.org/media/1246/06-attachment-a-sc-logistics-plan.pdf.Google Scholar
• Seraphin H (2019) Natural disaster and destination management: The case of the Caribbean and hurricane Irma. Current Issues Tourism 22(1):21–28.Crossref, Google Scholar
• Shapiro A, Nemirovski A (2005) On complexity of stochastic programming problems. Jeyakumar V, Rubinov A, eds. Continuous Optimization: Current Trends and Modern Applications (Springer, Berlin), 111–146.Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczynski A (2021) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).Crossref, Google Scholar
• Siddig M, Song Y (2025) Multistage stochastic programming with a random number of stages: Applications in hurricane disaster relief logistics planning. Eur. J. Oper. Res. 321(3):925–941.Crossref, Google Scholar
• Taskin S, Lodree EJ Jr (2010) Inventory decisions for emergency supplies based on hurricane count predictions. Internat. J. Production Econom. 126(1):66–75.Crossref, Google Scholar
• Yang H, Duque D, Morton DP (2022) Optimizing diesel fuel supply chain operations to mitigate power outages for hurricane relief. IISE Trans. 1–14.Google Scholar
• Zhang S, Sun XA (2022) Stochastic dual dynamic programming for multistage stochastic mixed-integer nonlinear optimization. Math. Programming 1–51.Google Scholar
• Zou J, Ahmed S, Sun XA (2018) Multistage stochastic unit commitment using stochastic dual dynamic integer programming. IEEE Trans. Power Systems 34(3):1814–1823.Crossref, Google Scholar
• Zou J, Ahmed S, Sun XA (2019) Stochastic dual dynamic integer programming. Math. Programming 175(1):461–502.Crossref, Google Scholar
• Zverovich V, Fábián CI, Ellison EF, Mitra G (2012) A computational study of a solver system for processing two-stage stochastic LPs with enhanced Benders decomposition. Math. Programming Comput. 4(3):211–238.Crossref, Google Scholar