Mathematical Programming

, Volume 156, Issue 1–2, pp 343–389

Combining sampling-based and scenario-based nested Benders decomposition methods: application to stochastic dual dynamic programming

Full Length Paper Series A

DOI: 10.1007/s10107-015-0884-3

Cite this article as:
Rebennack, S. Math. Program. (2016) 156: 343. doi:10.1007/s10107-015-0884-3


Nested Benders decomposition is a widely used and accepted solution methodology for multi-stage stochastic linear programming problems. Motivated by large-scale applications in the context of hydro-thermal scheduling, in 1991, Pereira and Pinto introduced a sampling-based variant of the Benders decomposition method, known as stochastic dual dynamic programming (SDDP). In this paper, we embed the SDDP algorithm into the scenario tree framework, essentially combining the nested Benders decomposition method on trees with the sampling procedure of SDDP. This allows for the incorporation of different types of uncertainties in multi-stage stochastic optimization while still maintaining an efficient solution algorithm. We provide an illustration of the applicability of our method towards a least-cost hydro-thermal scheduling problem by examining an illustrative example combining both fuel cost with inflow uncertainty and by studying the Panama power system incorporating both electricity demand and inflow uncertainties.


Stochastic dual dynamic programming Hydro-thermal power system  Nested Benders decomposition Sampling Scenario tree  Electricity demand and inflow uncertainty 

Mathematics Subject Classification

90C15 90C05 90C39 90C90 

Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2015

Authors and Affiliations

  1. 1.Division of Economics and BusinessColorado School of MinesGoldenUSA

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