scholarly journals Single-stage gradient-based stellarator coil design: stochastic optimization

2021 ◽  
Author(s):  
Florian Wechsung ◽  
Andrew Giuliani ◽  
M. Landreman ◽  
Antoine J Cerfon ◽  
Georg Stadler
Keyword(s):  
Stochastic Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Numerical Study ◽  
Single Stage ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Coil Design ◽  
Risk Neutral ◽  
Gradient Based

Abstract We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into account coil manufacturing errors. By modeling coil errors independently from the coil discretization, we have the flexibility to consider realistic forms of coil errors. The corresponding stochastic optimization problems are formulated using a risk-neutral approach and risk-averse approaches. We present an efficient, gradient-based descent algorithm which relies on analytical derivatives to solve these problems. In a comprehensive numerical study, we compare the coil designs resulting from deterministic and risk-neutral stochastic optimization and find that the risk-neutral formulation results in more robust configurations and reduces the number of local minima of the optimization problem. We also compare deterministic and risk-neutral approaches in terms of quasi-symmetry on and away from the magnetic axis, and in terms of the confinement of particles released close to the axis. Finally, we show that for the optimization problems we consider, a risk-averse objective using the Conditional Value-at-Risk leads to results which are similar to the risk-neutral objective.

Coordinating Vulnerable Supply Chains with Option Contracts

2021 ◽  
pp. 2050053
Author(s):  
Zhongyi Liu ◽  
Shengya Hua ◽  
Guanying Wang
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Numerical Study ◽  
Supply Chain Coordination ◽  
Wholesale Price ◽  
Conditional Value At Risk ◽  
Option Contract ◽  
Risk Neutral ◽  
Disruption Risk

We investigate vulnerable supply chain coordination with an option contract in the presence of supply chain disruption risk caused by external and internal disturbances. The supply chain consists of a single risk-neutral supplier and a risk-averse retailer. We characterize the retailer’s order quantity decision under the Conditional Value-at-Risk (CVaR) criterion and the supplier’s production decision. The results show that facing disruption risk and risk-aversion, both the retailer and the supplier would be more prudent to order and produce less than the risk-neutral scenario, inducing damage to the supply chain performance. The number of options purchased is decreasing in disruption risk and the risk-aversion of the retailer. The supplier will increase production as the disruption risk decreases or the shortage penalty increases. When the supplier does not know the risk-aversion of the retailer, the former will produce more and bear a higher overstock risk. We also investigate conditions that facilitate vulnerable supply chain coordination and find that the existence of risk-aversion and disruption risk restrict the option price and exercise price to lower price levels. Finally, we compare the option contract with wholesale price contract from the supplier’s and retailer’s perspectives through a numerical study.

OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

2021 ◽  
pp. 1-29
Author(s):  
Yanhong Chen
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Numerical Study ◽  
Risk Measure ◽  
Convex Combination ◽  
Weighting Factor ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Optimal Reinsurance ◽  
The Impact

ABSTRACT In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

scholarly journals Risk-Averse Multi-Stage Stochastic Programming to Optimizing Vaccine Allocation and Treatment Logistics for Effective Epidemic Response

2021 ◽  
Author(s):  
Xuecheng Yin ◽  
Esra Buyuktahtakin
Keyword(s):  
Value At Risk ◽  
Virus Disease ◽  
Risk Measure ◽  
Adverse Outcomes ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Expected Number ◽  
Multi Stage ◽  
Stochastic Mixed Integer Programming

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

Coordinating Supply Chain with Buy-Back Contracts in the Presence of Risk Aversion

2018 ◽  
Vol 35 (02) ◽  
pp. 1840008 ◽  
Author(s):  
Chunlin Luo ◽  
Xin Tian ◽  
Xiaobing Mao ◽  
Qiang Cai
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Performance Measure ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Allocation Rule ◽  
Risk Averse ◽  
Buy Back ◽  
The Impact

This paper addresses the operational decisions and coordination of the supply chain in the presence of risk aversion, where the risk averse retailer’s performance is measured by a combination of the expected profit and conditional value-at-risk (CVaR). Such performance measure reflects the desire of the retailer to maximize the expected profit on one hand and to control the downside risk of the profit on the other hand. The impact of risk aversion on the supply chain’s decision and performance is also explored. To overcome the inefficiency due to the double marginalization and the aggravation resulting from risk aversion, we investigate the buy-back contract to coordinate the supply chain. Such contract can largely increase the supply chain’s profit, especially when the retailer is more risk averse. Lastly, we extend such risk measure to the widely-used business model nowadays — platform selling model, and explore the impact of the allocation rule on the manufacturer’s decision.

scholarly journals Financial Risk Control of Hydro Generation Systems through Market Intelligence and Stochastic Optimization

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6368
Author(s):  
Laís Domingues Leonel ◽  
Mateus Henrique Balan ◽  
Dorel Soares Ramos ◽  
Erik Eduardo Rego ◽  
Rodrigo Ferreira de Mello
Keyword(s):  
Stochastic Optimization ◽  
Utility Function ◽  
Value At Risk ◽  
Financial Risk ◽  
Conditional Value At Risk ◽  
Spot Price ◽  
Model Formulation ◽  
Wholesale Market ◽  
Market Intelligence ◽  
Risk Metric

In the competitive electricity wholesale market, decisions regarding hydro generators are generally made under uncertain conditions, such as pool price, hydrological affluence, and other players’ strategies. From this perspective, this work presents a computational model formulation with associated market intelligence and game theory tools to support a decision-making process in a competitive environment. The idea behind using a market intelligence tool is to apply a stochastic optimization model with an associated conditional value at risk metric defining a utility function, which calculates the weight that the agents attribute to each stochastic variable associated with the problem to be faced. Subsequently, this utility function is used to emulate the other agents’ strategies based on their previous decisions. The final step finds the Nash equilibrium solution between a player and their competitors. The methodology is applied to the monthly allocation of firm energy by hydro generators under the current Brazilian regulatory framework. The results show a change in the generators’ behavior over the years, from risk-neutral agents seeking to maximize their return with 88% of decisions based on spot price forecasts in 2015, to risk-averse agents with 100% of decisions following a factor that is directly impacted by the hydrological affluence forecasts in 2018.

scholarly journals A stochastic design optimization methodology to reduce emission spread in combustion engines

2020 ◽  
Author(s):  
Kadir Mourat ◽  
Carola Eckstein ◽  
Thomas Koch
Keyword(s):  
Monte Carlo ◽  
Stochastic Optimization ◽  
Value At Risk ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Learning Algorithm ◽  
Main Idea ◽  
Design Parameters ◽  
Engine Calibration ◽  
Deterministic Setting

AbstractThis paper introduces a method for efficiently solving stochastic optimization problems in the field of engine calibration. The main objective is to make more conscious decisions during the base engine calibration process by considering the system uncertainty due to component tolerances and thus enabling more robust design, low emissions, and avoiding expensive recalibration steps that generate costs and possibly postpone the start of production. The main idea behind the approach is to optimize the design parameters of the engine control unit (ECU) that are subject to uncertainty by considering the resulting output uncertainty. The premise is that a model of the system under study exists, which can be evaluated cheaply, and the system tolerance is known. Furthermore, it is essential that the stochastic optimization problem can be formulated such that the objective function and the constraint functions can be expressed using proper metrics such as the value at risk (VaR). The main idea is to derive analytically closed formulations for the VaR, which are cheap to evaluate and thus reduce the computational effort of evaluating the objective and constraints. The VaR is therefore learned as a function of the input parameters of the initial model using a supervised learning algorithm. For this work, we employ Gaussian process regression models. To illustrate the benefits of the approach, it is applied to a representative engine calibration problem. The results show a significant improvement in emissions compared to the deterministic setting, where the optimization problem is constructed using safety coefficients. We also show that the computation time is comparable to the deterministic setting and is orders of magnitude less than solving the problem using the Monte-Carlo or quasi-Monte-Carlo method.

Optimal Option Purchasing Decisions for the Risk-Averse Retailer with Shortage Cost

2019 ◽  
Vol 36 (02) ◽  
pp. 1940005 ◽  
Author(s):  
Xin-Sheng Xu ◽  
Felix T. S. Chan
Keyword(s):  
Confidence Level ◽  
Value At Risk ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Purchasing Decisions ◽  
Shortage Cost ◽  
High Return ◽  
Potential Risks ◽  
Purchase Quantity

To hedge against potential risks, this paper introduces the conditional value-at-risk (CVaR) measure into the option purchasing for the risk-averse retailer with shortage cost. We introduce two models for the risk-averse retailer to select the optimal option purchase quantity. It is found that both two optimal option purchase quantities to two models can be decreasing in the retail price and increasing in the option executing price under certain conditions. This is different from the optimal option purchase quantity for a risk-neutral retailer to maximize the expected profit. It is found that both two optimal option purchase quantities may be increasing or decreasing in the confidence level, which implies a retailer who becomes more risk-averse may purchase more or fewer options to hedge against potential risks. Under both two optimal option purchase quantities, it is proven that the retailer’s expected profit is decreasing in the confidence level. This confirms the fact that high return implies high risk while low risk comes with low return.

SUPPLY CHAIN COORDINATION WITH CVaR CRITERION

2009 ◽  
Vol 26 (01) ◽  
pp. 135-160 ◽  
Author(s):  
LEI YANG ◽  
MINGHUI XU ◽  
GANG YU ◽  
HANQIN ZHANG
Keyword(s):  
Supply Chain ◽  
Value At Risk ◽  
Supply Chain Coordination ◽  
Revenue Sharing ◽  
Retail Price ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Mild Conditions ◽  
Quantity Flexibility ◽  
Buy Back

We study the coordination of supply chains with a risk-neutral supplier and a risk-averse retailer. Different from the downside risk setting, in a conditional value-at-risk (CVaR) framework, we show that the supply chain can be coordinated with the revenue-sharing, buy-back, two-part tariff and quantity flexibility contracts. Furthermore the revenue-sharing contracts are still equivalent to the buy-back contracts when the retail price is fixed. At the same time, it is shown that the risk-averse retailer of the coordinated supply chain can increase its profit by raising its risk-averse degree under mild conditions.

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