Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision mak...
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Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision making. We propose a computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in AC power systems. Our approach uses recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian structure. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal policy of the stochastic AC-OPF problem as long as the SDP relaxations are tight. To test the practical viability of our approach, we set up a case study of a storage siting, sizing, and operations problem. We show that the convex SDP relaxation of the stochastic problem is usually tight and discuss ways to obtain near-optimal physically feasible solutions when this is not the case. The algorithm finds a physically feasible policy with an optimality gap of 3% and yields a significant added value of 27% over a rolling deterministic policy, which leads to overly optimistic policies and underinvestment in flexibility. This suggests that the common industry practice of assuming direct current and deterministic problems should be reevaluated by considering models that incorporate realistic AC flows and stochastic elements in the data as potentially more realistic alternatives.
Supply contracts are known as the communication link among supply chain members. As sourcing of required goods is a challenging issue for supply chain members, different sourcing types for different market conditions ...
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Supply contracts are known as the communication link among supply chain members. As sourcing of required goods is a challenging issue for supply chain members, different sourcing types for different market conditions have been presented in the literature. However, the uncertain price condition has not been much focused in the previous studies, and in the limited works on this issue the correlation between the periods has been ignored. In this paper, sourcing policies are analyzed in a multi-period system in which price and demand follow a Geometric Brownian Motion with drift. Wholesale contract, option contract, and purchase from the spot market are considered as the sourcing alternatives for the buyer. This paper applies the stochastic programming approach to model these three types of sourcing based upon price and demand uncertainties. Afterwards, a hybrid supply model of these sourcing types is developed. By a numerical example, the simulation results of the developed models reveal that each individual sourcing alternative can be selected as the best one in each price and demand behavior. The results also suggest that the proposed hybrid model dominates each of the individual sourcing types. Finally, the paper reports the effects of cost parameter alterations on the solution of the hybrid model through sensitivity analysis. (C) 2015 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
The unexpected aircraft failure is one of the main disruption factors that cause flight irregularity. The aircraft schedule recovery is a challenging problem in both industrial and academic fields, especially when air...
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The unexpected aircraft failure is one of the main disruption factors that cause flight irregularity. The aircraft schedule recovery is a challenging problem in both industrial and academic fields, especially when aircraft restoration time is uncertain, which is often ignored in previous research. This paper established a two-stage stochastic recovery model to deal with the problem. The first stage model was a resource assignment model on aircraft schedule recovery, with the objective function of minimizing delay and cancellation cost. The second stage model used simple retiming strategy to adjust the aircraft routings obtained in the first stage, with the objective function of minimizing the expected cost on recourse decision. Based on different scenarios of restoration time, the second stage model can be degenerated as several linear models. A stochastic Greedy Simulated Annealing algorithm was designed to solve the model. The computational results indicate that the proposed stochastic model and algorithm can effectively improve the feasibility of the recovery solutions, and the analysis of value of stochastic solution shows that the stochastic model is worthy of implementation in real life.
stochastic programming models are large-scale optimization problems that are used to facilitate decision making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs o...
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stochastic programming models are large-scale optimization problems that are used to facilitate decision making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integral whose integrand is an optimization problem. In turn, the recourse function has to be estimated using techniques such as scenario trees or Monte Carlo methods, both of which require numerous functional evaluations to produce accurate results for large-scale problems with multiple periods and high-dimensional uncertainty. In this work, we introduce an importance sampling framework for stochastic programming that can produce accurate estimates of the recourse function using a small number of samples. Our framework combines Markov chain Monte Carlo methods with kernel density estimation algorithms to build a nonparametric importance sampling distribution, which can then be used to produce a lower-variance estimate of the recourse function. We demonstrate the increased accuracy and efficiency of our approach using variants of well-known multistage stochastic programming problems. Our numerical results show that our framework produces more accurate estimates of the optimal value of stochastic programming models, especially for problems with moderate variance, multimodal, or rare-event distributions.
Several approaches for the Bayesian design of experiments have been proposed in the literature (e.g., D-optimal, E-optimal, A-optimal designs). Most of these approaches assume that the available prior knowledge is rep...
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Several approaches for the Bayesian design of experiments have been proposed in the literature (e.g., D-optimal, E-optimal, A-optimal designs). Most of these approaches assume that the available prior knowledge is represented by a normal probability distribution. In addition, most nonlinear design approaches involve assuming normality of the posterior distribution and approximate its variance using the expected Fisher information matrix. In order to be able to relax these assumptions, we address and generalize the problem by using a stochastic programming formulation. Specifically, the optimal Bayesian experimental design is mathematically posed as a three-stage stochastic program, which is then discretized using a scenario based approach. Given the prior probability distribution, a Smolyak rule (sparse-grids) is used for the selection of scenarios. Two retrospective case studies related to population pharmacokinetics are presented. The benefits and limitations of the proposed approach are demonstrated by comparing the numerical results to those obtained by implementing a more exhaustive experimentation and the D-optimal design. (C) 2014 Elsevier Ltd. All rights reserved.
This paper presents an detailed study about the development of an integrative DR policy for the optimal home energy management system under stochastic *** this study,home appliances are classified into three categorie...
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ISBN:
(纸本)9781467397155
This paper presents an detailed study about the development of an integrative DR policy for the optimal home energy management system under stochastic *** this study,home appliances are classified into three categories and detailed modeling of all kinds of home appliances is ***,the optimal HEMS problem is formulated as a stochastic programming model considering the uncertainties of PV production and critical loads to minimize a customer's electricity *** Carlo simulation method is used to decompose the problem into a mixed integer linear programming ***,the proposed stochastic programming model is verified through numerical *** simulation results show that the proposed stochastic DR model can reduce the effect of the uncertainties in residential environment on the electricity cost and obtain a better DR policy than the conventional deterministic model.
We consider bounds for the price of a European-style call option under regime switching. stochastic semidefinite programming models are developed that incorporate a lattice generated by a finite-state Markov chain reg...
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We consider bounds for the price of a European-style call option under regime switching. stochastic semidefinite programming models are developed that incorporate a lattice generated by a finite-state Markov chain regime-switching model as a representation of scenarios (uncertainty) to compute bounds. The optimal first-stage bound value is equivalent to a Value at Risk quantity, and the optimal solution can be obtained via simple sorting. The upper (lower) bounds from the stochastic model are bounded below (above) by the corresponding deterministic bounds and are always less conservative than their robust optimization (min-max) counterparts. In addition, penalty parameters in the model allow controllability in the degree to which the regime switching dynamics are incorporated into the bounds. We demonstrate the value of the stochastic solution (bound) and computational experiments using the S&P 500 index are performed that illustrate the advantages of the stochastic programming approach over the deterministic strategy.
The author considers the use of risk measures that allows combining stochastic programming and robust optimization problems within the overall approach. Constructions for the class of polyhedral coherent risk measures...
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The author considers the use of risk measures that allows combining stochastic programming and robust optimization problems within the overall approach. Constructions for the class of polyhedral coherent risk measures are described. It is shown how the use of such measures can reduce problems of linear optimization under uncertainty to deterministic linear programming problems.
This paper focuses on the energy optimal operation problem of microgrids (MGs) under stochastic environment. The deterministic method of MGs operation is often uneconomical because it fails to consider the high random...
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This article presents a model to assist decision makers in the logistics of a flood emergency. The model attempts to optimize inventory levels for emergency supplies as well as vehicles' availability, in order to ...
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This article presents a model to assist decision makers in the logistics of a flood emergency. The model attempts to optimize inventory levels for emergency supplies as well as vehicles' availability, in order to deliver enough supplies to satisfy demands with a given probability. A spatio-temporal stochastic process represents the flood occurrence. The model is approximately solved with sample average approximation. The article presents a method to quantify the impact of the various intervening logistics parameters. An example is provided and a sensitivity analysis is performed. The studied example shows large differences between the impacts of logistics parameters such as number of products, number of periods, inventory capacity and degree of demand fulfillment on the logistics cost and time. This methodology emerges as a valuable tool to help decision makers to allocate resources both before and after a flood occurs, with the aim of minimizing the undesirable effects of such events. (C) 2014 Elsevier Ltd. All rights reserved.
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