We revisit the sample average approximation (SAA) approach for nonconvex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result ...
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We revisit the sample average approximation (SAA) approach for nonconvex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic optimality guarantees as the sample size increases. To address this issue, we relax the equality constraints. Then, we prove the asymptotic optimality of the modified SAA approach under mild smoothness and boundedness conditions on the equality constraint functions. Our analysis uses random set theory and concentration inequalities to characterize the approximation error from the sampling procedure. We apply our approach and analysis to the problem of stochastic optimal control for nonlinear dynamical systems under external disturbances modeled by a Wiener process. Numerical results on relevant stochastic programs show the reliability of the proposed approach. Results on a rocket-powered descent problem show that our computed solutions allow for significant uncertainty reduction compared to a deterministic baseline.
In this study, an interval fixed-mix stochastic programming (IFSP) model is developed for greenhouse gas (GHG) emissions reduction management under uncertainties. In the IFSP model, methods of interval-parameter progr...
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In this study, an interval fixed-mix stochastic programming (IFSP) model is developed for greenhouse gas (GHG) emissions reduction management under uncertainties. In the IFSP model, methods of interval-parameter programming (IPP) and fixed-mix stochastic programming (FSP) are introduced into an integer programming framework, such that the developed model can tackle uncertainties described in terms of interval values and probability distributions over a multi-stage context. Moreover, it can reflect dynamic decisions for facility-capacity expansion during the planning horizon. The developed model is applied to a case of planning GHG-emission mitigation, demonstrating that IFSP is applicable to reflecting complexities of multi-uncertainty, dynamic and interactive energy management systems, and capable of addressing the problem of GHG-emission reduction. A number of scenarios corresponding to different GHG-emission mitigation levels are examined;the results suggest that reasonable solutions have been generated. They can be used for generating plans for energy resource/electricity allocation and capacity expansion and help decision makers identify desired GHG mitigation policies under various economic costs and environmental requirements. (C) 2010 Elsevier Ltd. All rights reserved.
With the growing global energy demand and worsening ecological environment, coal-abundant countries are actively developing the technologies which could convert coal to liquid fuels, so called coal-to liquids (CTL), t...
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With the growing global energy demand and worsening ecological environment, coal-abundant countries are actively developing the technologies which could convert coal to liquid fuels, so called coal-to liquids (CTL), to adjust and optimize energy structure, guarantee energy security, and reduce environmental pollution. For the optimal planning of a CTL supply chain, a two-stage stochastic programming model is established to maximize the profit of the CTL supply chain under the products demand uncertainty. Various technical and operational constraints involving the infrastructure construction, CTL plants production, products and coal transport as well as the influence of products oversupply, are considered in the model. Based on the sample average approximation method, a number of finite scenarios for the uncertain parameters are generated, the established stochastic model is converted into an equivalent deterministic model and then solved. Finally, the model was successfully applied to a real world CTL supply chain in Sinkiang, China. The applicability of the proposed model was testified. Also, comparative studies were carried out to illustrate the influence of the uncertainty on the CTL supply chain. (C) 2019 Elsevier Ltd. All rights reserved.
Large corporations fund their capital and operational expenses by issuing bonds with a variety of indexations, denominations, maturities and amortization schedules. We propose a multistage linear stochastic programmin...
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Large corporations fund their capital and operational expenses by issuing bonds with a variety of indexations, denominations, maturities and amortization schedules. We propose a multistage linear stochastic programming model that optimizes bond issuance by minimizing the mean funding cost while keeping leverage under control and insolvency risk at an acceptable level. The funding requirements are determined by a fixed investment schedule with uncertain cash flows. Candidate bonds are described in a detailed and realistic manner. A specific scenario tree structure guarantees computational tractability even for long horizon problems. Based on a simplified example, we present a sensitivity analysis of the first stage solution and the stochastic efficient frontier of the mean-risk trade-off. A realistic exercise stresses the importance of controlling leverage. Based on the proposed model, a financial planning tool has been implemented and deployed for Brazilian oil company Petrobras. (C) 2014 Elsevier B.V. All rights reserved.
We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method...
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We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region method. The parallel platform of choice is the dynamic, heterogeneous, opportunistic platform provided by the Condor system. The algorithms are of master-worker type (with the workers being used to solve second-stage problems), and the MW runtime support library (which supports master-worker computations) is key to the implementation. Computational results are presented on large sample-average approximations of problems from the literature.
The problem of minimax optimization of a linear functional with random coefficients with respect to a probabilistic criterion under deterministic constraints is considered. The information about the distribution law o...
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The problem of minimax optimization of a linear functional with random coefficients with respect to a probabilistic criterion under deterministic constraints is considered. The information about the distribution law of the vector of random model parameters is restricted only to specifying some sets of uncertainty of its expectation and covariance matrix. The concept of constructing a minimax control function is based on transition to a dual problem. The analytic dependence of the minimax control function on "the worst" parameters of the distribution of random coefficients is given. The obtained technical results are illustrated by examples.
The International Conference on Water and the Environment held in Dublin in 1992 emphasized the need to consider water as an economic good. Since water markets are usually absent or ineffective, the value of water can...
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The International Conference on Water and the Environment held in Dublin in 1992 emphasized the need to consider water as an economic good. Since water markets are usually absent or ineffective, the value of water cannot be directly derived from market activities but must rather be assessed through shadow prices. Economists have developed various valuation techniques to determine the economic value of water, especially to handle allocation issues involving environmental water uses. Most of the nonmarket valuation studies reported in the literature focus on long-run policy problems, such as permanent (re) allocations of water, and assume that the water availability is given. When dealing with short-run allocation problems, water managers are facing complex spatial and temporal trade-offs and must therefore be able to track site and time changes in water values across different hydrologic conditions, especially in arid and semiarid areas where the availability of water is a limiting and stochastic factor. This paper presents a stochastic programming approach for assessing the statistical distribution of marginal water values in multipurpose multireservoir systems where hydropower generation and irrigation crop production are the main economic activities depending on water. In the absence of a water market, the Lagrange multipliers correspond to shadow prices, and the marginal water values are the Lagrange multipliers associated with the mass balance equations of the reservoirs. The methodology is illustrated with a cascade of hydroelectric-irrigation reservoirs in the Euphrates river basin in Turkey and Syria.
We propose a multistage stochastic programming model to optimally allocate cargo to the passengers network in order to maximize profit, taking into account incomes, costs and penalties for not delivering cargo that wa...
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We propose a multistage stochastic programming model to optimally allocate cargo to the passengers network in order to maximize profit, taking into account incomes, costs and penalties for not delivering cargo that was previously accepted. Flights have a discrete number of possible capacity outcomes, with known probabilities, and uncertainty is represented by a scenario tree. The resulting problem is a large-scale linear program, and we use decomposition techniques to solve it, leveraging on the problem structure in order to be able to find good quality solutions. Our numerical experiments are based on a real network of a major commercial airline.
While raising debt on behalf of the government. public debt managers need to consider several possibly conflicting objectives and have to find an appropriate combination for government debt taking into account the unc...
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While raising debt on behalf of the government. public debt managers need to consider several possibly conflicting objectives and have to find an appropriate combination for government debt taking into account the uncertainty with regard to the future state of the economy. In this paper, we explicitly consider the underlying uncertainties with a complex multi-period stochastic programming model that captures the trade-offs between the objectives. The model is designed to aid the decision makers in formulating the debt issuance strategy. We apply an interactive procedure that guides the issuer to identify good strategies and demonstrate this approach for the public debt management problem of Turkey. (C) 2009 Elsevier B.V. All rights reserved.
Make-to-order firms use different strategies, such as dynamic pricing and due date management, to influence their performance. In these strategies, orders are segmented into classes based on their sensitivity to lead ...
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Make-to-order firms use different strategies, such as dynamic pricing and due date management, to influence their performance. In these strategies, orders are segmented into classes based on their sensitivity to lead time and price. Quoting different prices and lead times to different classes of customer can increase a firm's profit and its capacity utilization. Most research in this area does not consider the effects of production constraints on price and lead time decisions. In this paper, we consider the role of flexibility in dynamically choosing the price, lead time and segmentation of customers in make-to-order environments with limited production capacity and multi-period horizon under a stochastic demand function. To reflect the dynamic variations of a system's conditions, we propose a Multi-stage stochastic programming (MSP) method to jointly determine prices, lead time and production. Furthermore, we assume that demand is a linear function of price, lead time and time. Through numerical analyses, we indicate the benefits of dynamic pricing and lead time decisions, based on different customer classes in various environments. (C) 2011 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.
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