This paper proposes two extensions to the SMPS format for stochastic programs to permit modelling of autoregressive-moving average (ARMA) processes. Sampling-based algorithms can thus proceed independently of any unde...
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This paper proposes two extensions to the SMPS format for stochastic programs to permit modelling of autoregressive-moving average (ARMA) processes. Sampling-based algorithms can thus proceed independently of any underlying modelling system, increasing efficiency. An illustrative example demonstrates the power of the new constructs.
This paper presents a stochastic linear programming framework for the hydropower portfolio management problem with uncertainty in market prices and inflows on medium term. The uncertainty is modeled as a scenario tree...
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This paper presents a stochastic linear programming framework for the hydropower portfolio management problem with uncertainty in market prices and inflows on medium term. The uncertainty is modeled as a scenario tree using the Monte Carlo simulation method, and the objective is to maximize the expected revenue over the entire scenario tree. The portfolio decisions of the stochastic model are formulated as a tradeoff involving different scenarios. Numerical results illustrate the impact of uncertainty on the portfolio management decisions, and indicate the significant value of stochastic solution. (C) 2009 Elsevier Ltd. All rights reserved.
In this study, an inventory-theory-based interval stochastic programming (IB-ISP) model is proposed through incorporating stochastic programming and interval parameters within an inventory model. IB-ISP can tackle unc...
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In this study, an inventory-theory-based interval stochastic programming (IB-ISP) model is proposed through incorporating stochastic programming and interval parameters within an inventory model. IB-ISP can tackle uncertainties expressed as probability density functions (PDFs) and interval parameters in constraints and objective function. The developed IB-ISP is then applied to planning electric-power generation system of Beijing. Support vector regression (SVR) is used for forecasting the electricity demand, which is useful for coping with the uncertainty of customer demand. During the coal transportation processes, various factors may affect the time consumption of coal transportation, leading to uncertainties existing in energy generation and energy inventory. Under different delay times of coal transportation, different safety stocks and inventory patterns are generated to minimize the system cost and ensure the regular operation of the coal-fired power plants. The results obtained can not only help the managers to identify desired policies for safety stock in electricity-generation processes, but also be used for minimizing system cost and generating desired inventory pattern (with optimal transferring batch and period). Compared with the traditional economic order quantity (EOQ) model, the IB-ISP model can provide an effective measure for not-timely coal supplying pattern with a reduced system-failure risk under uncertainty. (C) 2014 Elsevier Ltd. All rights reserved.
A virtual power plant aggregates various local production/consumption units that act in the market as a single entity. This paper considers a virtual power plant consisting of an intermittent source, a storage facilit...
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A virtual power plant aggregates various local production/consumption units that act in the market as a single entity. This paper considers a virtual power plant consisting of an intermittent source, a storage facility, and a dispatchable power plant. The virtual power plant sells and purchases electricity in both the day-ahead and the balancing markets seeking to maximize its expected profit. Such model is mathematically rigorous, yet computationally efficient. The offering problem is cast as a two-stage stochastic mixed-integer linear programming model which maximizes the virtual power plant expected profit. The uncertain parameters, including the power output of the intermittent source and the market prices, are modeled via scenarios based upon historical data. The proposed model is applied to a realistic case study and conclusions are drawn. Published by Elsevier Ltd.
In this paper, we develop a multi-objective stochastic programming approach for supply chain design under uncertainty. Demands, supplies, processing, transportation, shortage and capacity expansion costs are all consi...
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In this paper, we develop a multi-objective stochastic programming approach for supply chain design under uncertainty. Demands, supplies, processing, transportation, shortage and capacity expansion costs are all considered as the uncertain parameters. To develop a robust model, two additional objective functions are added into the traditional comprehensive supply chain design problem. So, our multi-objective model includes (i) the minimization of the sum of current investment costs and the expected future processing, transportation, shortage and capacity expansion costs, (ii) the minimization of the variance of the total cost and (iii) the minimization of the financial risk or the probability of not meeting a certain budget. The ideas of unreliable suppliers and capacity expansion, after the realization of uncertain parameters, are also incorporated into the model. Finally, we use the goal attainment technique to obtain the Pareto-optimal solutions that can be used for decision-making. (c) 2008 Elsevier B.V. All rights reserved.
The assignment of tasks to teams is a challenging combinatorial optimisation problem. The uncertainty in the tasks' execution processes further complicates the assignment decisions. This study investigates a varia...
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The assignment of tasks to teams is a challenging combinatorial optimisation problem. The uncertainty in the tasks' execution processes further complicates the assignment decisions. This study investigates a variant of the typical assignment problem, in which each task can be divided into two parts, one is deterministic and the other is uncertain with respect to their workloads. From the stochastic perspective, this paper proposes both a stochastic programming model that can cope with arbitrary probability distributions of tasks' random workload requirements, and a robust optimisation model that is applicable to situations in which limited information about probability distributions is available. An example of its application in the software project management is given. Some numerical experiments are also performed to validate the effectiveness of the proposed models and the relationships between the two models.
An LP is considered where the technology coefficients are unknown and random samples are taken to estimate them. A stochastic programming problem is formulated to find the optimal sample sizes where it is required tha...
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An LP is considered where the technology coefficients are unknown and random samples are taken to estimate them. A stochastic programming problem is formulated to find the optimal sample sizes where it is required that a confidence interval should cover the unknown deterministic optimum value by a given probability and the cost of sampling be minimum. (C) 2003 Elsevier B.V. All rights reserved.
This paper presents a bilevel programming approach to solve the medium-term decision-making problem faced by a power retailer. A retailer decides its level of involvement in the futures market and in the pool as well ...
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This paper presents a bilevel programming approach to solve the medium-term decision-making problem faced by a power retailer. A retailer decides its level of involvement in the futures market and in the pool as well as the selling price offered to its potential clients with the goal of maximizing the expected profit at a given risk level. Uncertainty on future pool prices, client demands, and rival-retailer prices is accounted for via stochastic programming. Unlike in previous approaches, client response to retail price and competition among rival retailers are both explicitly considered in the proposed bilevel model. The resulting nonlinear bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear programming problem by replacing the lower-level optimization by its Karush-Kuhn-Tucker optimality conditions and converting a number of nonlinearities to linear equivalents using some well-known integer algebra results. A realistic case study is solved to illustrate the efficient performance of the proposed methodology.
A nonlinear stochastic programming method is proposed in this article to deal with the uncertain optimization problems of overall ballistics. First, a general overall ballistic dynamics model is achieved based on clas...
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A nonlinear stochastic programming method is proposed in this article to deal with the uncertain optimization problems of overall ballistics. First, a general overall ballistic dynamics model is achieved based on classical interior ballistics, projectile initial disturbance calculation model, exterior ballistics and firing dispersion calculation model. Secondly, the random characteristics of uncertainties are simulated using a hybrid probabilistic and interval model. Then, a nonlinear stochastic programming method is put forward by integrating a back-propagation neural network with the Monte Carlo method. Thus, the uncertain optimization problem is transformed into a deterministic multi-objective optimization problem by employing the mean value, the standard deviation, the probability and the expected loss function, and then the sorting and optimizing of design vectors are realized by the non-dominated sorting genetic algorithm-II. Finally, two numerical examples in practical engineering are presented to demonstrate the effectiveness and robustness of the proposed method.
We present a stochastic programming framework for finding the optimal vaccination policy for controlling infectious disease epidemics under parameter uncertainty. stochastic programming is a popular framework for incl...
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We present a stochastic programming framework for finding the optimal vaccination policy for controlling infectious disease epidemics under parameter uncertainty. stochastic programming is a popular framework for including the effects of parameter uncertainty in a mathematical optimization model. The problem is initially formulated to find the minimum cost vaccination policy under a chance-constraint. The chance-constraint requires that the probability that R. <= I be greater than some parameter alpha, where R, is the post-vaccination reproduction number. We also show how to formulate the problem in two additional cases: (a) finding the optimal vaccination policy when vaccine supply is limited and (b) a cost-benefit scenario. The class of epidemic models for which this method can be used is described and we present an example formulation for which the resulting problem is a mixed-integer program. A short numerical example based on plausible parameter values and distributions is given to illustrate how including parameter uncertainty improves the robustness of the optimal strategy at the cost of higher coverage of the population. Results derived from a stochastic programming analysis can also help to guide decisions about how much effort and resources to focus on collecting data needed to provide better estimates of key parameters. (C) 2008 Elsevier Inc. All rights reserved.
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