In this paper a stochastic fundamental electricity market model is applied to estimate the integration costs of wind due to changed system operation and investments in Germany. The model's principle is cost minimi...
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In this paper a stochastic fundamental electricity market model is applied to estimate the integration costs of wind due to changed system operation and investments in Germany. The model's principle is cost minimization by determining the system costs mainly as a function of available generation and transmission capacities, primary energy prices, plant characteristics, and electricity demand. To obtain appropriate estimates of the integration costs notably reduced efficiencies at part load and start-up costs are taken into account. The intermittency of wind is covered by a stochastic recombining tree and the system is considered to adapt on increasing wind integration over time by endogenous modeling of reserve requirements and investments in thermal power plants. The results highlight the need for stochastic optimization models and the strong dependency on the actual system and its development over time to get sufficient estimates of the integration costs of wind's intermittency. Copyright (c) 2006 John Wiley & Sons, Ltd.
This article introduces a new exact algorithm for the capacitated vehicle routing problem with stochastic demands (CVRPSD). The CVRPSD can be formulated as a set partitioning problem and it is shown that the associate...
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This article introduces a new exact algorithm for the capacitated vehicle routing problem with stochastic demands (CVRPSD). The CVRPSD can be formulated as a set partitioning problem and it is shown that the associated column generation subproblem can be solved using a dynamic programming scheme. Computational experiments show promising results. (C) 2007 Elsevier B.V. All rights reserved.
This paper introduces a stochastic programming model that integrates strategic bids or offers for electricity (in quantities and prices) in a deregulated electricity market. The model is designed to maximize the profi...
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This paper introduces a stochastic programming model that integrates strategic bids or offers for electricity (in quantities and prices) in a deregulated electricity market. The model is designed to maximize the profits of a producer of electricity who manages a series of power plants along a river. The model is compared with a previously reported, stochastic model where the bidding process is disregarded. The superiority of the new model is empirically demonstrated on historical data.
Long-term power planning is a stochastic problem often confronted by electrical utilities in liberalized markets. One can model it for profit maximization-using market-price estimation functions for each interval-by p...
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Long-term power planning is a stochastic problem often confronted by electrical utilities in liberalized markets. One can model it for profit maximization-using market-price estimation functions for each interval-by posing it as a quadratic programming problem with some linear equalities and an exponential number of load-matching linear inequality constraints. In order to avoid handling all the inequalities when one is attempting to solve the problem, column generation methods have been employed herein. In this paper, we describe the foundations and implementation of a heuristic that tries to iteratively guess the active set of constraints at the optimizer, alongside a normal quadratic programming solution used at each iteration. The two methods are compared and the heuristic procedure is shown to be more efficient. (C) 2006 Elsevier B.V. All rights reserved.
In this paper, we extend the multi-period mean-variance optimization framework to worst-case design with multiple rival return and risk scenarios. Our approach involves a min-max algorithm and a multi-period mean-vari...
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In this paper, we extend the multi-period mean-variance optimization framework to worst-case design with multiple rival return and risk scenarios. Our approach involves a min-max algorithm and a multi-period mean-variance optimization framework for the stochastic aspects of the scenario tree. Multi-period portfolio optimization entails the construction of a scenario tree representing a discretised estimate of uncertainties and associated probabilities in future stages. The expected value of the portfolio return is maximized simultaneously with the minimization of its variance. There are two sources of further uncertainty that might require a strengthening of the robustness of the decision. The first is that some rival uncertainty scenarios may be too critical to consider in terms of probabilities. The second is that the return variance estimate is usually inaccurate and there are different rival estimates, or scenarios. In either case, the best decision has the additional property that, in terms of risk and return, performance is guaranteed in view of all the rival scenarios. The ex-ante performance of min-max models is tested using historical data and backtesting results are presented. (C) 2006 Elsevier B.V. All rights reserved.
Appropriate energy-environment-economic (E3) modelling provides key information for policy makers in the electricity supply industry (ESI) faced with navigating a sustainable development path. Key challenges include e...
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Appropriate energy-environment-economic (E3) modelling provides key information for policy makers in the electricity supply industry (ESI) faced with navigating a sustainable development path. Key challenges include engaging with stakeholder values and preferences, and exploring trade-offs between competing objectives in the face of underlying uncertainty. As a case study we represent the South African ESI using a partial equilibrium E3 modelling approach, and extend the approach to include multiple objectives under selected future uncertainties. This extension is achieved by assigning cost penalties to non-cost attributes to force the model's least-cost objective function to better satisfy non-cost criteria. This paper incorporates aspects of flexibility to demand growth uncertainty into each future expansion alternative by introducing stochastic programming with recourse into the model. Technology lead times are taken into account by the inclusion of a decision node along the time horizon where aspects of real options theory are considered within the planning process. Hedging in the recourse programming is automatically translated front being purely financial, to include the other attributes that the cost penalties represent. From a retrospective analysis of the cost penalties, the correct market signals, can be derived to meet policy goal, with due regard to demand uncertainty. (C) 2007 Elsevier Ltd. All rights reserved.
We propose a new scenario tree reduction algorithm for multistage stochastic programs, which integrates the reduction of a scenario tree into the solution process of the stochastic program. This allows to construct a ...
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We propose a new scenario tree reduction algorithm for multistage stochastic programs, which integrates the reduction of a scenario tree into the solution process of the stochastic program. This allows to construct a scenario tree that is highly adapted on the optimization problem. The algorithm starts with a rough approximation of the original tree and locally refines this approximation as long as necessary. Promising numerical results for scenario tree reductions in the settings of portfolio management and power management with uncertain load are presented.
In stochastic optimization problems, uncertainty is normally represented by means of a scenario tree. Finding an accurate representation of this uncertainty when dealing with a set of historical series is an important...
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In stochastic optimization problems, uncertainty is normally represented by means of a scenario tree. Finding an accurate representation of this uncertainty when dealing with a set of historical series is an important issue, because of its influence in the results of the above mentioned problems. This article uses a procedure to create the scenario tree divided into two phases: the first one produces a tree that represents accurately the original probability distribution, and in the second phase that tree is reduced to make it tractable. Several clustering methods are analysed and proposed in the paper to obtain the scenario tree. Specifically, these are applied to an academic case and to natural hydro inflows series, and comparisons amongst them are established according to these results. (C) 2006 Elsevier B.V. All rights reserved.
Multi-item inventory models with two storage facility and bulk release pattern are developed with linearly time dependent demand in a finite time horizon under crisp, stochastic and fuzzy-stochastic environments. Here...
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Multi-item inventory models with two storage facility and bulk release pattern are developed with linearly time dependent demand in a finite time horizon under crisp, stochastic and fuzzy-stochastic environments. Here different inventory parameters-holding costs, ordering costs, purchase costs, etc.-are assumed as probabilistic or fuzzy in nature. In particular cases stochastic and crisp models are derived. Models are formulated as profit maximization principle and three different approaches are proposed for solution. In the first approach, fuzzy extension principle is used to find membership function of the objective function and then it's Graded Mean Integration Value (GMIV) for different optimistic levels are taken as equivalent stochastic objectives. Then the stochastic model is transformed to a constraint multi-objective programming problem using stochastic Non-linear programming (SNLP) technique. The multi-objective problems are transferred to single objective problems using Interactive Fuzzy Satisfising (IFS) technique. Finally, a Region Reducing Genetic Algorithm (RRGA) based on entropy has been developed and implemented to solve the single objective problems. In the second approach, the above GMIV (which is stochastic in nature) is optimized with some degree of probability and using SNLP technique model is transferred to an equivalent single objective crisp problem and solved using RRGA. In the third approach, objective function is optimized with some degree of possibility/necessity and following this approach model is transformed to an equivalent constrained stochastic programming problem. Then it is transformed to an equivalent single objective crisp problem using SNLP technique and solved via RRGA. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.
With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper present...
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With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau-Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives. (c) 2006 Elsevier B.V. All rights reserved.
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