scholarly journals Scenario tree reduction in stochastic programming with recourse for hydropower operations

2015 ◽  
Vol 51 (8) ◽  
pp. 6359-6380 ◽  
Author(s):  
Bin Xu ◽  
Ping-An Zhong ◽  
Renato C. Zambon ◽  
Yunfa Zhao ◽  
William W.-G. Yeh
Keyword(s):  
Stochastic Programming ◽  
Scenario Tree ◽  
Stochastic Programming With Recourse

On the Scenario-Tree Optimal-Value Error for Stochastic Programming Problems

2020 ◽  
Vol 45 (4) ◽  
pp. 1572-1595
Author(s):  
Julien Keutchayan ◽  
David Munger ◽  
Michel Gendreau
Keyword(s):  
Stochastic Programming ◽  
Large Scale ◽  
Probability Distributions ◽  
Approximation Error ◽  
Scenario Tree ◽  
Branching Structures ◽  
Tree Generation ◽  
Optimal Value ◽  
Scenario Trees ◽  
Scenario Tree Generation

Stochastic programming problems generally lead to large-scale programs if the number of random outcomes is large or if the problem has many stages. A way to tackle them is provided by scenario-tree generation methods, which construct approximate problems from a reduced subset of outcomes. However, it is well known that the number of scenarios required to keep the approximation error within a given tolerance grows rapidly with the number of random parameters and stages. For this reason, to limit the fast growth of complexity, scenario-tree generation methods tailored to problems must be developed. These will use more information about the problem than just the underlying probability distributions; namely, they will also take into account the objective function and the constraints. In this paper, we develop a general framework to build problem-driven scenario trees. We do so by studying how the optimal-value error arises as a sum of lower-level errors made at each node of the tree. We show how these small but numerous node errors depend on the specific features of the problem and how they can be controlled by designing scenario trees with appropriate branching structures and discretization points and weights. We illustrate our approach on two examples.

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