A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the object...
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A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the objective function coefficients or the right hand side coefficients are continuous random vectors with known probability distributions. This is the “wait and see” problem of stochastic linear programming. Explicit results for the distribution problem are extremely difficult to obtain;indeed, previous results are known only if the right hand side coefficients have an exponential distribution [1]. To date, no explicit results have been obtained for stochastic c, and no new results of any form have appeared since the 1970’s. In this paper, we obtain the first results for stochastic c, and new explicit results if b an c are stochastic vectors with an exponential, gamma, uniform, or triangle distribution. A transformation is utilized that greatly reduces computational time.
We consider pricing of American contingent claims (ACC) as well as their special cases, in a multi-period, discrete time, discrete state space setting. Until now, determining the buyer's price for ACCs required so...
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We consider pricing of American contingent claims (ACC) as well as their special cases, in a multi-period, discrete time, discrete state space setting. Until now, determining the buyer's price for ACCs required solving an integer programme unlike European contingent claims for which solving a linear programme is sufficient. However, we show that a relaxation of the integer programming problem that is a linear programme, can be used to get the same lower bound for the price of the ACC.
Two-Stage stochasticlinear program with recourse is represented as a convex programming problem. The problem is often large-scale because involves an expectation. Moreover objective function is not necessary differen...
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Two-Stage stochasticlinear program with recourse is represented as a convex programming problem. The problem is often large-scale because involves an expectation. Moreover objective function is not necessary differentiable. In order to reduce difficulties in solving, the inner problem is approached by quadratic problem which are differentiable and are least two-norm solution problem of inner recourse linear problem. This paper proposes newton method to obtain least two-norm solution of recourse problems by using penalty problem of recourse problem.
This paper introduces a mean profit- conditional value-at-risk (CVaR) model for purchasing electricity on the day-ahead market (DA) by electric vehicles fleet aggregator (EVA). EVA controls electric vehicles (EVs) dur...
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This paper introduces a mean profit- conditional value-at-risk (CVaR) model for purchasing electricity on the day-ahead market (DA) by electric vehicles fleet aggregator (EVA). EVA controls electric vehicles (EVs) during their workplace parking, enabling smart charging and cost savings by accessing market prices that are potentially lower than flat rates available during home charging. The proposed stochastic linear programming model leverages market price scenarios to optimize aggregated charging schedules, which serve as templates for constructing effective DA bidding curves. It integrates an aspiration/reservation-based formulation of the mean profit-risk criteria, specifically Conditional Value at Risk (CVaR) to address the EVA's risk aversion. By incorporating interactive analysis, the framework ensures adaptive and robust charging schedules and bids tailored to the aggregator's risk preferences. Its ability to balance profitability with risk is validated in case studies. This approach provides a practical and computationally efficient tool for EV aggregators of global companies that can benefit from the workplace charging their fleets thanks to buying energy in the DA market.
This paper introduces a novel approach to blind adaptive equalization for digital communication systems using genetic algorithms (GAs). Unlike traditional methods that rely on linearprogramming and suffer from local ...
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This paper introduces a novel approach to blind adaptive equalization for digital communication systems using genetic algorithms (GAs). Unlike traditional methods that rely on linearprogramming and suffer from local minima issues, this technique utilizes a stochastic linear programming cost function with GAs for robust optimization. The proposed method termed Blind linear Equalizer based on genetic algorithm (BLE-GA) enhances performance by leveraging a GA's ability to handle stochastic variables, offering rapid convergence and resilience against signal noise and inter-symbol interference. Extensive simulations demonstrate the effectiveness of BLE-GA across different QAM systems, outperforming conventional techniques like the Constant Modulus Algorithm in scenarios with high modulation levels. This study validates the potential of using GAs in adaptive blind equalization to achieve reliable and efficient communication, even in complex and noisy channel conditions.
This study proposes a two-stage stochasticprogramming model to plan the transportation of vital first-aid commodities to disaster-affected areas during emergency response. A multi-commodity, multi-modal network flow ...
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This study proposes a two-stage stochasticprogramming model to plan the transportation of vital first-aid commodities to disaster-affected areas during emergency response. A multi-commodity, multi-modal network flow formulation is developed to describe the flow of material over an urban transportation network. Since it is difficult to predict the timing and magnitude of any disaster and its impact on the urban system, resource mobilization is treated in a random manner, and the resource requirements are represented as random variables. Furthermore, uncertainty arising from the vulnerability of the transportation system leads to random arc capacities and supply amounts. Randomness is represented by a finite sample of scenarios for capacity, supply and demand triplet. The two stages are defined with respect to information asymmetry, which discloses uncertainty during the progress of the response. The approach is validated by quantifying the expected value of perfect and stochastic information in problem instances generated out of actual data.
Ariyawansa and Zhu have recently proposed a new class of optimization problems termed stochastic semidefinite programs (SSDPs). SSDPs may be viewed as an extension of two-stage stochastic (linear) programs with recour...
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Ariyawansa and Zhu have recently proposed a new class of optimization problems termed stochastic semidefinite programs (SSDPs). SSDPs may be viewed as an extension of two-stage stochastic (linear) programs with recourse (SLPs). Zhao has derived a decomposition algorithm for SLPs based on a logarithmic barrier and proved its polynomial complexity. Mehrotra and Ozevin have extended the work of Zhao to the case of SSDPs to derive a polynomial logarithmic barrier decomposition algorithm for SSDPs. An alternative to the logarithmic barrier is the volumetric barrier of Vaidya. There is no work based on the volumetric barrier analogous to that of Zhao for SLPs or to the work of Mehrotra and Ozevin for SSDPs. The purpose of this paper is to derive a class of volumetric barrier decomposition algorithms for SSDPs, and to prove polynomial complexity of certain members of the class.
We consider a cash management problem where a company with a given financial endowment and given future cash flows minimizes the Conditional Value at Risk of final wealth using a lower bound for the expected terminal ...
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We consider a cash management problem where a company with a given financial endowment and given future cash flows minimizes the Conditional Value at Risk of final wealth using a lower bound for the expected terminal wealth. We formulate the optimization problem as a multi-stage stochasticlinear program (SLP). The company can choose between a riskless asset (cash), several default- and option-free bonds, and an equity investment, and rebalances the portfolio at every stage. The uncertainty faced by the company is reflected in the development of interest rates and equity returns. Our model has two new features compared to the existing literature, which uses no-arbitrage interest rate models for the scenario generation. First, we explicitly estimate a function for the market price of risk and change the underlying probability measure. Second, we simulate scenarios for equity returns with moment-matching by an extension of the interest rate scenario tree.
作者:
BEREANU, BUNIV BONN
SONDER FORSCH BEREICH 72D-5300 BONN 1FED REP GER MINIST EDUC
CTR MATH STATISTICSBUCHARESTROMANIA
It is proved a sufficient condition that the optimal value of a linear program be a continuous function of the coefficients. The condition isessential, in the sense that, if it is not imposed, then examples with disco...
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It is proved a sufficient condition that the optimal value of a linear program be a continuous function of the coefficients. The condition isessential, in the sense that, if it is not imposed, then examples with discontinuous optimal-value function may be found. It is shown that certain classes of linear programs important in applications satisfy this condition. Using the relation between parametric linearprogramming and the distribution problem in stochasticprogramming, a necessary and sufficient condition is given that such a program has optimal value. Stable stochasticlinear programs are introduced, and a sufficient condition of such stability, important in computation problems, is established.
We investigate the quality of solutions obtained from sample-average approximations to two-stage stochasticlinear programs with recourse. We use a recently developed software tool executing on a computational grid to...
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We investigate the quality of solutions obtained from sample-average approximations to two-stage stochasticlinear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain high-quality solutions and to verify optimality and near-optimality of the computed solutions in various ways.
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