The benefits of cooperation under uncertainty: the case of climate change

This article presents an analysis of the behavior of countries defining their climate policies in an uncertain context. The analysis is made using the S-CWS model, a stochastic version of an integrated assessment growth model. The model includes a stochastic definition of the climate sensitivity parameter. We show that the impact of uncertainty on policy design critically depends on the shape of the damage function. We also examine the benefits of cooperation in the context of uncertainty: we highlight the existence of an additional benefit of cooperation, namely risk reduction.cooperation, uncertainty, climate change, integrated assessment model

Optimal day-ahead offering strategy for large producers based on market price response learning

In day-ahead electricity markets based on uniform marginal pricing, small variations in the offering and bidding curves may substantially modify the resulting market outcomes. In this work, we deal with the problem of finding the optimal offering curve for a risk-averse profit-maximizing generating company (GENCO) in a data-driven context. In particular, a large GENCO's market share may imply that her offering strategy can alter the marginalprice formation, which can be used to increase profit. We tackle this problem from a novel perspective. First, we propose a optimization-based methodology to summarize each GENCO's step-wise supply curves into a subset of representative price-energy blocks. Then, the relationship between the market price and the resulting energy block offering prices is modeled through a Bayesian linear regression approach, which also allows us to generate stochastic scenarios for the sensibility of the market towards the GENCO strategy, represented by the regression coefficient probabilistic distributions. Finally, this predictive model is embedded in the stochastic optimization model by employing a constraint learning approach. Results show how allowing the GENCO to deviate from her true marginal costs renders significant changes in her profits and the market marginal price. Furthermore,these results have also been tested in an out-of-sample validation setting, showing how this optimal offering strategy is also effective in a real-world market contest

A practical assessment of risk-averse approaches in production lot-sizing problems

This paper presents an empirical assessment of four state-of-the-art risk-averse approaches to deal with the capacitated lot-sizing problem under stochastic demand. We analyse two mean-risk models based on the semideviation and on the conditional value-at-risk risk measures, and alternate first and second-order stochastic dominance approaches. The extensive computational experiments based on different instances characteristics and on a case-study suggest that CVaR exhibits a good trade-off between risk and performance, followed by the semideviation and first-order stochastic dominance approach. For all approaches, enforcing risk-aversion helps to reduce the cost-standard deviation substantially, which is usually accomplished via increasing production rates. Overall, we can say that very risk-averse decision-makers would be willing to pay an increased price to have a much less risky solution given by CVaR. In less risk-averse settings, though, semideviation and first-order stochastic dominance can be appealingalternatives to provide significantly more stable production planning costs with a marginal increase of the expected costs.Peer reviewe

Multi-Period Asset Allocation: An Application of Discrete Stochastic Programming

The issue of modeling farm financial decisions in a dynamic framework is addressed in this paper. Discrete stochastic programming is used to model the farm portfolio over the planning period. One of the main issues of discrete stochastic programming is representing the uncertainty of the data. The development of financial scenario generation routines provides a method to model the stochastic nature of the model. In this paper, two approaches are presented for generating scenarios for a farm portfolio problem. The approaches are based on copulas and optimization. The copula method provides an alternative to the multivariate normal assumption. The optimization method generates a number of discrete outcomes which satisfy specified statistical properties by solving a non-linear optimization model. The application of these different scenario generation methods is then applied to the topic of geographical diversification. The scenarios model the stochastic nature of crop returns and land prices in three separate geographic regions. The results indicate that the optimal diversification strategy is sensitive to both scenario generation method and initial acreage assumptions. The optimal diversification results are presented using both scenario generation methods.Agribusiness, Agricultural Finance, Farm Management,

Model Reduction of Synchronized Lur'e Networks

In this talk, we investigate a model order reduction schemethat reduces the complexity of uncertain dynamical networks consisting of diffusively interconnected nonlinearLure subsystems. We aim to reduce the dimension ofeach subsystem and meanwhile preserve the synchronization property of the overall network. Using the upperbound of the Laplacian spectral radius, we first characterize the robust synchronization of the Lure network bya linear matrix equation (LMI), whose solutions can betreated as generalized Gramians of each subsystem, andthus the balanced truncation can be performed on the linear component of each Lure subsystem. As a result, thedimension of the each subsystem is reduced, and the dynamics of the network is simplified. It is verified that, withthe same communication topology, the resulting reducednetwork system is still robustly synchronized, and the apriori bound on the approximation error is guaranteed tocompare the behaviors of the full-order and reduced-orderLure subsyste

Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak's algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments

On the time-consistent stochastic dominance risk averse measure for tactical supply chain planning under uncertainty

In this work a modeling framework and a solution approach have been presented for a multi-period stochastic mixed 0–1 problem arising in tactical supply chain planning (TSCP). A multistage scenario tree based scheme is used to represent the parameters’ uncertainty and develop the related Deterministic Equivalent Model. A cost risk reduction is performed by using a new time-consistent risk averse measure. Given the dimensions of this problem in real-life applications, a decomposition approach is proposed. It is based on stochastic dynamic programming (SDP). The computational experience is twofold, a compar- ison is performed between the plain use of a current state-of-the-art mixed integer optimization solver and the proposed SDP decomposition approach considering the risk neutral version of the model as the subject for the benchmarking. The add-value of the new risk averse strategy is confirmed by the compu- tational results that are obtained using SDP for both versions of the TSCP model, namely, risk neutral and risk averse.The authors would like to thank to the two anonymous review- ers for their help on clarifying some concepts presented in the manuscript and strongly improving its presentatio