Scenario Tree Approximation and Risk Aversion Strategies for Stochastic Optimization of Electricity Production and Trading

2009 ◽  
pp. 321-346 ◽  
Author(s):  
Andreas Eichhorn ◽  
Holger Heitsch ◽  
Werner Römisch
Keyword(s):  
Risk Aversion ◽  
Stochastic Optimization ◽  
Scenario Tree ◽  
Electricity Production ◽  
Tree Approximation

Design of hydrogen supply chains under demand uncertainty – a case study of passenger transport in Germany

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anton Ochoa Bique ◽  
Leonardo K. K. Maia ◽  
Ignacio E. Grossmann ◽  
Edwin Zondervan
Keyword(s):  
Stochastic Optimization ◽  
Demand Uncertainty ◽  
Programming Model ◽  
Cost Minimization ◽  
Water Electrolysis ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Strong Impact ◽  
Hydrogen Supply

Abstract A strategy for the design of a hydrogen supply chain (HSC) network in Germany incorporating the uncertainty in the hydrogen demand is proposed. Based on univariate sensitivity analysis, uncertainty in hydrogen demand has a very strong impact on the overall system costs. Therefore we consider a scenario tree for a stochastic mixed integer linear programming model that incorporates the uncertainty in the hydrogen demand. The model consists of two configurations, which are analyzed and compared to each other according to production types: water electrolysis versus steam methane reforming. Each configuration has a cost minimization target. The concept of value of stochastic solution (VSS) is used to evaluate the stochastic optimization results and compare them to their deterministic counterpart. The VSS of each configuration shows significant benefits of a stochastic optimization approach for the model presented in this study, corresponding up to 26% of infrastructure investments savings.

scholarly journals Stochastic scenario generation: An empirical approach

2018 ◽  
Author(s):  
A. D. Oliveira ◽  
T. P. Filomena
Keyword(s):  
Monte Carlo ◽  
Stochastic Optimization ◽  
Random Sampling ◽  
Sampling Method ◽  
Empirical Approach ◽  
Scenario Tree ◽  
Scenario Generation ◽  
Distinctive Features

We briefly discuss the differences among several methods to generate a scenario tree for stochastic optimization. First, the Monte Carlo Random sampling is presented, followed by the Fitting of the First Two Moments sampling, and lastly the Michaud sampling. Literature results are reviewed, taking into account distinctive features of each kind of methodology. According to the literature results, it is fundamental to consider the problem’s unique characteristics to make the more appropriate choice on sampling method.  

Robust Stochastic Optimization Made Easy with RSOME

2020 ◽  
Vol 66 (8) ◽  
pp. 3329-3339 ◽  
Author(s):  
Zhi Chen ◽  
Melvyn Sim ◽  
Peng Xiong
Keyword(s):  
Robust Optimization ◽  
Stochastic Optimization ◽  
Linear Optimization ◽  
Mixture Distribution ◽  
Scenario Tree ◽  
Distributionally Robust Optimization ◽  
Clustering And Classification ◽  
Stochastic Linear Optimization ◽  
Distributionally Robust ◽  
Generalized Moments

We present a new distributionally robust optimization model called robust stochastic optimization (RSO), which unifies both scenario-tree-based stochastic linear optimization and distributionally robust optimization in a practicable framework that can be solved using the state-of-the-art commercial optimization solvers. We also develop a new algebraic modeling package, Robust Stochastic Optimization Made Easy (RSOME), to facilitate the implementation of RSO models. The model of uncertainty incorporates both discrete and continuous random variables, typically assumed in scenario-tree-based stochastic linear optimization and distributionally robust optimization, respectively. To address the nonanticipativity of recourse decisions, we introduce the event-wise recourse adaptations, which integrate the scenario-tree adaptation originating from stochastic linear optimization and the affine adaptation popularized in distributionally robust optimization. Our proposed event-wise ambiguity set is rich enough to capture traditional statistic-based ambiguity sets with convex generalized moments, mixture distribution, φ-divergence, Wasserstein (Kantorovich-Rubinstein) metric, and also inspire machine-learning-based ones using techniques such as K-means clustering and classification and regression trees. Several interesting RSO models, including optimizing over the Hurwicz criterion and two-stage problems over Wasserstein ambiguity sets, are provided. This paper was accepted by David Simchi-Levi, optimization.

scholarly journals Risk Analysis for Reservoir Real-Time Optimal Operation Using the Scenario Tree-Based Stochastic Optimization Method

Water ◽  
2018 ◽  
Vol 10 (5) ◽  
pp. 606 ◽  
Author(s):  
Yimeng Sun ◽  
Feilin Zhu ◽  
Juan Chen ◽  
Jinshu Li
Keyword(s):  
Risk Analysis ◽  
Stochastic Optimization ◽  
Real Time ◽  
Flood Control ◽  
Forecast Accuracy ◽  
Optimization Method ◽  
Optimal Operation ◽  
Scenario Tree ◽  
Analysis Model ◽  
Time Optimal

The inherent uncertainty of inflow forecasts hinders the reservoir real-time optimal operation. This paper proposes a risk analysis model for reservoir real-time optimal operation using the scenario tree-based stochastic optimization method. We quantify the probability distribution of inflow forecast uncertainty by developing the relationship between two forecast accuracy metrics and the standard deviation of relative forecast error. An inflow scenario tree is generated via Monte Carlo simulation to represent the uncertain inflow forecasts. We establish a scenario tree-based stochastic optimization model to explicitly incorporate inflow forecast uncertainty into the stochastic optimization process. We develop a risk analysis model based on the principle of maximum entropy (POME) to evaluate the uncertainty propagation process from flood forecasts to optimal operation. We apply the proposed methodology to a flood control system in the Daduhe River Basin, China. In addition, numerical experiments are carried out to investigate the effect of two different forecast accuracy metrics and different forecast accuracy levels on reservoir optimal flood control operation as well as risk analysis. The results indicate that the proposed methods can provide decision-makers with valuable risk information for guiding reservoir real-time optimal operation and enable risk-informed decisions to be made with higher reliabilities.

scholarly journals Stochastic Optimization Model for Detailed Long-term Hydro Thermal Scheduling Using Scenario-tree Simulation

2016 ◽  
Vol 87 ◽  
pp. 165-172 ◽  
Author(s):  
Geir Warland ◽  
Birger Mo
Keyword(s):  
Stochastic Optimization ◽  
Optimization Model ◽  
Scenario Tree

Risk aversion and land allocation between annual and perennial crops in semisubsistence farming: a stochastic optimization approach

2019 ◽  
Vol 50 (3) ◽  
pp. 329-339 ◽  
Author(s):  
Pierre D. Ouattara ◽  
Eugene Kouassi ◽  
Aklesso Y. G. Egbendéwé ◽  
Oluyele Akinkugbe
Keyword(s):  
Risk Aversion ◽  
Stochastic Optimization ◽  
Land Allocation ◽  
Optimization Approach ◽  
Perennial Crops

Stochastic Optimization of Electricity Portfolios: Scenario Tree Modeling and Risk Management

2010 ◽  
pp. 405-432 ◽  
Author(s):  
Andreas Eichhorn ◽  
Holger Heitsch ◽  
Werner Römisch
Keyword(s):  
Risk Management ◽  
Stochastic Optimization ◽  
Scenario Tree ◽  
Tree Modeling

Weber's law predicts risk aversion for amounts and risk proneness for delay

1997 ◽  
Author(s):  
Alex Kacelnik
Keyword(s):  
Risk Aversion ◽  
Weber’S Law ◽  
Weber's Law
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