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Robust reservoir operation has long been considered a promising solution for addressing water allocation problems in the absence of reliable hydroclimatic forecasts. This study aims to evaluate the performance of this solution using a novel two-stage stochastic optimization model. The model maximizes economic benefits from reservoir deliveries while integrating stochastic inflows into a water allocation system with multiple demands and various constraints. The outcome of the model is a robust set of monthly reservoir releases that perform well under a wide range of hydroclimatic conditions. The model has been applied to the case of the Big Bend Reach of the Rio Grande/Bravo, a transboundary river basin of high importance for Mexico and the United States. The performance of the robust operation policy was assessed by comparing its outcome to those obtained under observed historical operations and an operation policy derived from a deterministic version of the optimization model that assumes perfect hydroclimatic knowledge. The results of this study indicate that the set of robust releases developed here outperforms historical reservoir operations and performs similarly to operations under perfect knowledge. These results show the effectiveness of robust reservoir operation and the usefulness of the proposed optimization model for decision-making under increasing hydroclimatic uncertainty. [ABSTRACT FROM AUTHOR]

Interdependencies among land use systems resemble a complex network connected through demand-supply relationships. Disruption of this network may catalyse systemic risks affecting food, energy, water and environmental security ( FEWES) worldwide. We describe the conceptual development, expansion and practical application of a stochastic version of the Global Biosphere Management Model ( GLOBIOM), used to assess competition for land use between agriculture, bioenergy and forestry at regional and global scales. In the stochastic version of the model, systemic risks of various kinds are explicitly covered and can be analysed and mitigated in all their interactions. While traditional deterministic scenario analysis produces sets of scenario-dependent outcomes, stochastic GLOBIOM explicitly derives robust outcomes that leave the systems better-off, independently of which scenario applies. Stochastic GLOBIOM is formulated as a stochastic optimisation model that is critical for evaluating portfolios of robust interdependent decisions: ex-ante strategic decisions (production allocation, storage capacities) and ex-post adaptive (demand, trading, storage control) decisions. As an example, the model is applied to the question of optimal storage facilities, as buffers for production shortfalls, to meet regional and global FEWES requirements when extreme events occur. Expected shortfalls and storage capacities have a close relationship with Value-at-Risk (VaR) and Conditional Value-at-Risk ( CVaR) risk measures. A Value of Stochastic Solutions is calculated to illustrate the benefits of the stochastic over the deterministic model approach. [ABSTRACT FROM AUTHOR]

Due to deregulations of the energy sector and the setting of targets such as the 20/20/20 in the EU, operators of public buildings are now more exposed to instantaneous (short-term) market conditions. On the other hand, they have gained the opportunity to play a more active role in securing long-term supply, managing demand, and hedging against risk while improving existing buildings' infrastructures. Therefore, there are incentives for the operators to develop and use a Decision Support System to manage their energy sub-systems in a more robust energy-efficient and cost-effective manner. In this paper, a two-stage stochastic model is proposed, where some decisions (so-called first-stage decisions) regarding investments in new energy technologies have to be taken before uncertainties are resolved, and some others (so-called second-stage decisions) on how to use the installed technologies will be taken once values for uncertain parameters become known, thereby providing a trade-off between long- and short-term decisions. [ABSTRACT FROM AUTHOR]

The paper studies stochastic optimization (programming) problems with compound functions containing expectations and extreme values of other random functions as arguments. Compound functions arise in various applications. A typical example is a variance function of nonlinear outcomes. Other examples include stochastic minimax problems, econometric models with latent variables, and multilevel and multicriteria stochastic optimization problems. As a solution technique a sample average approximation (SAA) method (also known as statistical or empirical (sample) mean method) is used. The method consists in approximation of all expectation functions by their empirical means and solving the resulting approximate deterministic optimization problems. In stochastic optimization, this method is widely used for optimization of standard expectation functions under constraints. In this paper, SAA method is extended to general compound stochastic optimization problems. The conditions for convergence in mean, almost surely, and rate of convergence are established. The study of the convergence rate is based on properties of Rademacher averages of functional sets, concentration inequalities for bounded random functions, and the concept of uniform normalized convergence of random variables. The convergence results are applicable both for discrete and continuous stochastic optimization problems. [ABSTRACT FROM AUTHOR]

The idea of market-based carbon emission trading and carbon taxes is gaining in popularity as a global climate change policy instrument. However, these mechanisms might not necessarily have a positive outcome unless their value reflects socioeconomic and environmental impacts and regulations. Moreover, the fact that they have various inherent exogenous and endogenous uncertainties raises serious concerns about their ability to reduce emissions in a cost-effective way. This paper aims to introduce a simple stochastic model that allows the robustness of economic mechanisms for emission reduction under multiple natural and human-related uncertainties to be analyzed. Unlike standard equilibrium state analysis, the model shows that the explicit introduction of uncertainties regarding emissions, abatement costs, and equilibrium states makes it almost impossible for existing market-based trading and carbon taxes to be environmentally safe and cost-effective. Here we propose a computerized multi-agent trading model. This can be viewed as a prototype to simulate an emission trading market that is regulated in a decentralized way. We argue that a market of this type is better equipped to deal with long-term emission reductions, their direct regulation, irreversibility, and 'lock-in' equilibria. [ABSTRACT FROM AUTHOR]

The paper analyzes the implications of extreme events on the proper choice of discounting. Any discounting with constant or declining rates can be linked to random “stopping time” events, which define the internal discount-related horizons of evaluations. Conversely, any stopping time induces a discounting, in particular, with the standard discount rates. The expected duration of the stopping time horizon for discount rates obtained from capital markets does not exceed a few decades and, as such, these rates may significantly underestimate the net benefits of long-term decisions. The alternative undiscounted stopping time criterion allows to induce social discounting focusing on arrival times of potential extreme events rather then horizons of market interests. Induced discount rates are conditional on the degree of social commitment to mitigate risk. In general, extreme events affect these rates, which alter the optimal mitigation efforts that, in turn, change events. The use of undiscounted stopping time criteria requires stochastic optimisation methods. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate the need for risk-adjusted approaches to planning expansion of livestock production. In particular, we illustrate that under exposure to risk, a portfolio of producers is needed where more efficient producers co-exist and cooperate with less efficient ones given that the latter are associated with lower, uncorrelated or even negatively correlated contingencies. This raises important issues of cooperation and risk sharing among diverse producers. For large-scale practical allocation problems when information on the contingencies may be disperse, not analytically tractable, or be available on aggregate levels, we propose a downscaling procedure based on behavioral principles utilizing spatial risk preference structure. It allows for estimation of production allocation at required resolutions accounting for location specific risks and suitability constraints. The approach provides a tool for harmonization of data from various spatial levels. We applied the method in a case study of livestock production allocation in China to 2030. [ABSTRACT FROM AUTHOR]

The Kyoto Protocol foresees emission trading but does not yet specify verification of (uncertain) emissions. This paper analyses a setting in which parties can meet their emission targets by reducing emissions, by investing in monitoring (reducing uncertainty of emissions) or by (bilaterally) trading permits. We derive the optimality conditions and carry out various numerical simulations. Our applications suggest that including uncertainty could increase compliance costs for the USA, Japan and the European Union. Central Europe and the Former Soviet Union might be able to gain from trading due to higher permit prices. Emissions trading could also lower aggregate uncertainty on emissions. [ABSTRACT FROM AUTHOR]

Uncertainty and variability are key challenges for climate change adaptation planning. In the face of uncertainty, decision-making can be addressed in two interdependent stages: make only partial ex ante anticipative actions to keep options open until new information is revealed, and adapt the first-stage decisions with respect to newly acquired information. This decision-making approach corresponds to the two-stage stochastic optimization (STO) incorporating both anticipative ex ante and adaptive ex post decisions within a single model. This paper develops a two-stage STO model for climate change adaptation through robust land use and irrigation planning under conditions of uncertain water supply. The model identifies the differences between decision-making in the cases of perfect information, full uncertainty, and two-stage STO from the perspective of learning about uncertainty. Two-stage anticipative and adaptive decision-making with safety constraints provides risk-informed decisions characterized by quantile-based Value-at-Risk and Conditional Value-at-Risk risk measures. The ratio between the ex ante and ex post costs and the shape of uncertainty determine the balance between the anticipative and adaptive decisions. Selected numerical results illustrate that the alteration of the ex ante agricultural production costs can affect crop production, management technologies, and natural resource utilization. [ABSTRACT FROM AUTHOR]

Traditional integrated modeling (IM) is based on developing and aggregating all relevant (sub)models and data into a single integrated linear programming (LP) model. Unfortunately, this approach is not applicable for IM under asymmetric information (ASI), i.e., when "private" information regarding sectoral/regional models is not available, or it cannot be shared by modeling teams (sectoral agencies). The lack of common information about LP submodels makes LP methods inapplicable for integrated LP modeling. The aim of this paper is to develop a new approach to link and optimize distributed sectoral/regional optimization models, providing a means of decentralized cross-sectoral coordination in the situation of ASI. Thus, the linkage methodology enables the investigation of policies in interdependent systems in a "decentralized" fashion. For linkage, the sectoral/regional models do not need recoding or reprogramming. They also do not require additional data harmonization tasks. Instead, they solve their LP submodels independently and in parallel by a specific iterative subgradient algorithm for nonsmooth optimization. The submodels continue to be the same separate LP models. A social planner (regulatory agency) only needs to adjust the joint resource constraints to simple subgradient changes calculated by the algorithm. The approach enables more stable and resilient systems' performance and resource allocation as compared to the independent policies designed by separate models without accounting for interdependencies. The paper illustrates the application of the methodology to link detailed energy and agricultural production planning models under joint constraints on water and land use. [ABSTRACT FROM AUTHOR]

The optimal allocation of indivisible resources is formalized as a stochastic optimization problem involving discrete decision variables. A general stochastic search procedure is proposed, which develops the concept of the branch-and-bound method. The main idea is to process large collections of possible solutions and to devote more attention to the most promising groups. By gathering more information to reduce the uncertainty and by narrowing the search area, the optimal solution can be found with probability one. Special techniques for calculating stochastic lower and upper bounds are discussed. The results are illustrated by a computational experiment. [ABSTRACT FROM AUTHOR]

A new concept of (normalized) convergence of random variables is introduced. This convergence is preserved under Lipschitz transformations, follows from convergence in mean and itself implies convergence in probability. If a sequence of random variables satisfies a limit theorem then it is a normalized convergent sequence. The introduced concept is applied to the convergence rate study of a statistical approach in stochastic optimization. [ABSTRACT FROM AUTHOR]

A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single surrogate inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration continues. This general aggregation principle is incorporated into a number of specific algorithms. Convergence of the new methods is proved and speed of convergence analyzed. Next, dual interpretation of the method is provided and application to decomposable problems is discussed. Finally, a numerical illustration is given. [ABSTRACT FROM AUTHOR]

Critical imbalances and threshold exceedances can trigger a disruption in a network of interdependent systems. An insignificant-at-first-glance shock can induce systemic risks with cascading catastrophic impacts. Systemic risks challenge traditional risk assessment and management approaches. These risks are shaped by systemic interactions, risk exposures, and decisions of various agents. The paper discusses the need for the two-stage stochastic optimization (STO) approach that enables the design of a robust portfolio of precautionary strategic and operational adaptive decisions that makes the interdependent systems flexible and robust with respect to risks of all kinds. We established a connection between the robust quantile-based non-smooth estimation problem in statistics and the two-stage non-smooth STO problem of robust strategic–adaptive decision-making. The coexistence of complementary strategic and adaptive decisions induces systemic risk aversion in the form of Value-at-Risk (VaR) quantile-based risk constraints. The two-stage robust decision-making is implemented into a large-scale Global Biosphere Management (GLOBIOM) model, showing that robust management of systemic risks can be addressed by solving a system of probabilistic security equations. Selected numerical results emphasize that a robust combination of interdependent strategic and adaptive solutions presents qualitatively new policy recommendations, if compared to a traditional scenario-by-scenario decision-making analysis. [ABSTRACT FROM AUTHOR]