This paper addresses the self-scheduling problem of a hydrothermal producer, which is formulated and solved as a two-stage stochastic programming problem with recourse in order to account for market uncertainty. The p...
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ISBN:
(纸本)9781627483889
This paper addresses the self-scheduling problem of a hydrothermal producer, which is formulated and solved as a two-stage stochastic programming problem with recourse in order to account for market uncertainty. The producer is considered to own thermal and hydro generating units and participate as a price-maker in the day-ahead energy market. Forward bilateral contracts with end-consumers are considered and their effect on the producer self-schedule and profits is examined. The CVaR metric accounting for risk management is also incorporated. Post-processing techniques are applied for the construction of the generating units optimal offer curves to be submitted to the day-ahead energy market.
One of the most important objectives of a manufacturing firm is the efficient design and operation of its supply chain to maximize profit. Paper is an example of a valuable material that can be recycled and recovered....
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One of the most important objectives of a manufacturing firm is the efficient design and operation of its supply chain to maximize profit. Paper is an example of a valuable material that can be recycled and recovered. Uncertainty is one of the characteristics of the real world. The methods that cope with uncertainty help researchers get realistic results. In this study, a two-stagestochastic programing model is proposed to determine a long term strategy including optimal facility locations and optimal flow amounts for large scale reverse supply chain network design problem under uncertainty. This network design problem includes optimal recycling and collection center locations and optimal flow amounts between the nodes in the multi-facility environment. Proposed model is suitable for recycling/manufacturing type of systems in reverse supply chain. All deterministic, stochastic models are mixed-integer programing models and are solved by commercial software GAMS 21.6/CPLEX 9.0.
We present an algorithm for shape optimization under stochastic loading and representative numerical results. Our strategy builds upon a combination of techniques from two-stage stochastic programming and level-set-ba...
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We present an algorithm for shape optimization under stochastic loading and representative numerical results. Our strategy builds upon a combination of techniques from two-stage stochastic programming and level-set-based shape optimization. In particular, usage of linear elasticity and quadratic objective functions permits us to obtain a computational cost which scales linearly in the number of linearly independent applied forces, which often is much smaller than the number of different realizations of the stochastic forces. Numerical computations are performed using a level set method with composite finite elements both in two and in three spatial dimensions.
An inexact two-stagestochastic robust programming model (ITSRP) was developed in this study for dealing with water resources allocation problems under uncertainty. ITSRP was formulated based on integration of interva...
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An inexact two-stagestochastic robust programming model (ITSRP) was developed in this study for dealing with water resources allocation problems under uncertainty. ITSRP was formulated based on integration of interval linear programming (ILP), stochastic robust optimization (SRO), and two-stage stochastic programming (TSP) techniques. It could deal with uncertainties expressed as not only probability distributions but also discrete intervals, and could facilitate analyses of the policy scenarios that are associated with economic penalties when the predefined policies were violated. Moreover, the variability measure about the second-stage penalty costs was incorporated into the objective function, such that the trade-off between system economy and stability could be evaluated. The developed model was applied to a hypothetical case of water resources management system. Results demonstrated that the ITSRP model could help decision makers generate stable and balanced water resources allocation patterns, gain in-depth insights into effects of the uncertainties, and analyze trade-offs between system economy and stability.
In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a twostagestochasticprogramming approach. We show th...
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In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a twostagestochasticprogramming approach. We show that under relatively mild assumptions the associated cooperative games are totally balanced. Finally, we consider several example situations. (C) 2009 Elsevier B.V. All rights reserved.
Rapid population growth and economy development have led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing pop...
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Rapid population growth and economy development have led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing population. In this study, an inexact programming method based on two-stage stochastic programming and interval-parameter programming is developed to obtain optimal water-allocation strategies for agricultural irrigation systems. It is capable of handling such problems where two-stage decisions need to be suggested under random- and interval-parameter inputs. An interactive solving procedure derived from conventional interval-parameter programming makes it possible for the impact of lower and upper bounds of interval inputs to be well reflected in the resulting solutions. An agricultural irrigation management problem is then provided to demonstrate the applicability, and reasonable solutions are obtained. Compared to the solutions from a representative interval-parameter programming model where only one decision-stage exists, the interval of optimized objective-function value is narrow, indicating more alternatives could be provided when water-allocation targets are rather high. However, chances of obtaining more benefits exist in association with a risk of paying more penalties;such a relationship becomes apparent when the variation of water availability is much intensive.
Zhao showed that the log barrier associated with the recourse function of two-stagestochastic linear programs behaves as a strongly self-concordant barrier and forms a self-concordant family on the first-stage soluti...
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Zhao showed that the log barrier associated with the recourse function of two-stagestochastic linear programs behaves as a strongly self-concordant barrier and forms a self-concordant family on the first-stage solutions. In this paper, we show that the recourse function is also strongly self-concordant and forms a self-concordant family for the two-stagestochastic convex quadratic programs with recourse. This allows us to develop Bender's decomposition based linearly convergent interior point algorithms. An analysis of such an algorithm is given in this paper.
In this paper we present a log-barrier method for solving two-stage quadratic stochastic programs. The mathematical model considered here can be used to present several real world applications, including financial and...
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In this paper we present a log-barrier method for solving two-stage quadratic stochastic programs. The mathematical model considered here can be used to present several real world applications, including financial and production planning problems. We discuss fundamental properties associated with the proposed algorithm and analyze the convergence and complexity of the algorithm. (c) 2004 Elsevier Inc. All rights reserved.
This work proposes a two-stage stochastic programming model with fixed recourse via scenario analysis with incorporation of risk management for an optimal midterm refinery planning that addresses three factors of unce...
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This work proposes a two-stage stochastic programming model with fixed recourse via scenario analysis with incorporation of risk management for an optimal midterm refinery planning that addresses three factors of uncertainties: prices of crude oil and saleable products (in the objective function), product demands (in the RHS coefficients), and product yields (in the LHS coefficients). Compensating slack variables and discrepancy costs are employed to explicitly account for constraints' violations to increase model tractability. Variance is adopted as the risk measure, with its shortcomings highlighted and mean-absolute deviation proposed as an improved alternative. A representative numerical example is illustrated.
In this work we present a global optimization algorithm for solving a class of large-scale nonconvex optimization models that have a decomposable structure. Such models, which are very expensive to solve to global opt...
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In this work we present a global optimization algorithm for solving a class of large-scale nonconvex optimization models that have a decomposable structure. Such models, which are very expensive to solve to global optimality, are frequently encountered in two-stage stochastic programming problems, engineering design, and also in planning and scheduling. A generic formulation and reformulation of the decomposable models is given. We propose a specialized deterministic branch-and-cut algorithm to solve these models to global optimality, wherein bounds on the global optimum are obtained by solving convex relaxations of these models with certain cuts added to them in order to tighten the relaxations. These cuts are based on the solutions of the sub-problems obtained by applying Lagrangean decomposition to the original nonconvex model. Numerical examples are presented to illustrate the effectiveness of the proposed method compared to available commercial global optimization solvers that are based on branch and bound methods.
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