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

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 deco...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical programming Vol. 156; no. 1-2; pp. 343 - 389
Main Author: Rebennack, Steffen
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2016
Springer Nature B.V
Subjects:
Algorithms
Benders decomposition
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Computer programming
Decomposition
Dynamic programming
Electricity
Full Length Paper
Hydroelectric plants
Inflow
Linear programming
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Numerical Analysis
Optimization
Random variables
Scheduling
Stochastic models
Stochasticity
Studies
Theoretical
Trees
Uncertainty
United States > US
Scenario tree
Hydro-thermal power system
Nested Benders decomposition
Electricity demand and inflow uncertainty
90C39
90C90
Stochastic dual dynamic programming
90C15
90C05
Sampling
ISSN:0025-5610, 1436-4646
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-015-0884-3