This study presents a factorial two-stage stochastic programming (FTSP) approach for supporting water resource management under uncertainty. FTSP is developed through the integration of factorial analysis and two-stag...
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This study presents a factorial two-stage stochastic programming (FTSP) approach for supporting water resource management under uncertainty. FTSP is developed through the integration of factorial analysis and two-stage stochastic programming (TSP) methods into a general modeling framework. It can handle uncertainties expressed as probability distributions and interval numbers. This approach has two advantages in comparison to conventional inexact TSP methods. Firstly, FTSP inherits merits of conventional inexact two-stage optimization approaches. Secondly, it can provide detailed effects of uncertain parameters and their interactions on the system performance. The developed FTSP method is applied to a hypothetical case study of water resources systems analysis. The results indicate that significant factors and their interactions can be identified. They can be further analyzed for generating water allocation decision alternatives in municipal, industrial and agricultural sectors. Reasonable water allocation schemes can thus be formulated based on the resulting information of detailed effects from various impact factors and their interactions. Consequently, maximized net system benefit can be achieved.
A microgrid is a small-scale version of a centralized power grid that generates, distributes and regulates electricity flow to local entities using distributed generation and the main grid. Distributed energy storage ...
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A microgrid is a small-scale version of a centralized power grid that generates, distributes and regulates electricity flow to local entities using distributed generation and the main grid. Distributed energy storage systems can be used to mitigate adverse effects of intermittent renewable sources in a microgrid in which operators dynamically adjust electricity procurement and storage decisions in response to randomlyevolving demand, renewable supply and pricing information. We formulate a multistage stochastic programming (SP) model whose objective is to minimize the expected total energy costs incurred within a microgrid over a finite planning horizon. The model prescribes the amount of energy to procure, store and discharge in each decision stage of the horizon. However, for even a moderate number of stages, the model is computationally intractable;therefore, we customize the stochastic dual dynamic programming (SDDP) algorithm to obtain high-quality approximate solutions. Computation times and optimization gaps are significantly reduced by implementing a dynamic cut selection procedure and a lower bound improvement scheme within the SDDP framework. An extensive computational study reveals significant cost savings as compared to myopic and non-storage policies, as well as policies obtained using a two-stage SP model. The study also demonstrates the scalability of our solution procedure.
The objective of the proposed article is to minimize the transportation costs of foods and medicines from different source points to different hospitals by applying stochastic mathematical programming model to a trans...
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The objective of the proposed article is to minimize the transportation costs of foods and medicines from different source points to different hospitals by applying stochastic mathematical programming model to a transportation problem in a multi-choice environment containing the parameters in all constraints which follow the Logistic distribution and cost coefficients of objective function are also multiplicative terms of binary variables. Using the stochastic programming approach, the stochastic constraints are converted into an equivalent deterministic one. A transformation technique is introduced to manipulate cost coefficients of objective function involving multi-choice or goals for binary variables with auxiliary constraints. The auxiliary constraints depends upon the consecutive terms of multi-choice type cost coefficient of aspiration levels. A numerical example is presented to illustrate the whole idea.
In this article, we study the generation and transmission maintenance scheduling problem under uncertainty. We propose a two-stage optimization model with the first stage for weekly maintenance scheduling and the seco...
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In this article, we study the generation and transmission maintenance scheduling problem under uncertainty. We propose a two-stage optimization model with the first stage for weekly maintenance scheduling and the second stage for hourly economic power dispatch. To address the future uncertainties associated with renewable energy penetration and electricity demand, we formulate the problem as a two-stage stochastic mixed-integer programming model and incorporate Conditional Value at Risk (CVaR) to control the risk of having extreme loss of demand. To facilitate practical implementation, we apply the Benders decomposition algorithm tailored for parallel computing as the solution approach for the problem. The maintenance decisions, computational performance, and optimality of the model are evaluated by case studies on IEEE test instances. An extensive sensitivity analysis of CVaR related parameters is performed to illustrate their impact on decisions and risk management. The results show that the proposed risk-constrained model can provide effective annual maintenance plans for both generators and transmission lines on a weekly basis, and the Benders decomposition algorithm is able to solve large-scale problem instances efficiently.
We consider the issue of call center scheduling in an environment where arrivals rates are highly variable, aggregate volumes are uncertain, and the call center is subject to a global service level constraint. This pa...
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We consider the issue of call center scheduling in an environment where arrivals rates are highly variable, aggregate volumes are uncertain, and the call center is subject to a global service level constraint. This paper is motivated by work with a provider of outsourced technical support services where call volumes exhibit significant variability and uncertainty. The outsourcing contract specifies a Service Level Agreement that must be satisfied over an extended period of a week or month. We formulate the problem as a mixed-integer stochastic program. Our model has two distinctive features. Firstly, we combine the server sizing and staff scheduling steps into a single optimization program. Secondly, we explicitly recognize the uncertainty in period-by-period arrival rates. We show that the stochastic formulation, in general, calculates a higher cost optimal schedule than a model which ignores variability, but that the expected cost of this schedule is lower. We conduct extensive experimentation to compare the solutions of the stochastic program with the deterministic programs, based on mean valued arrivals. We find that, in general, the stochastic model provides a significant reduction in the expected cost of operation. The stochastic model also allows the manager to make informed risk management decisions by evaluating the probability that the Service Level Agreement will be achieved. (C) 2010 Elsevier B.V. All rights reserved.
We present a multi-period stochastic mixed integer programming model for power generation scheduling in a day-ahead electricity market. The model considers various scenarios and integrates the idea of reserve shortage...
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We present a multi-period stochastic mixed integer programming model for power generation scheduling in a day-ahead electricity market. The model considers various scenarios and integrates the idea of reserve shortage pricing in real time. Instead of including all the possible scenarios, we parsimoniously select a certain number of scenarios to limit the size of the model. As realistic size models are still intractable for exact methods, we propose a heuristic solution methodology based on scenario-rolling that is capable of finding good quality feasible solutions within reasonable computation time.
Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Math Pro...
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Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Math Program A 106(3):423-432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem data is governed by independent uniform distributions. We show that Dyer and Stougie's proof is not correct, and we offer a correction which establishes the stronger result that even the approximate solution of such problems is #P-hard for a sufficiently high accuracy. We also provide new results which indicate that linear two-stage stochastic programs with random recourse seem even more challenging to solve.
Scenarios are indispensable ingredients for the numerical solution of stochastic programs. Earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probab...
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Scenarios are indispensable ingredients for the numerical solution of stochastic programs. Earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data. For linear two-stage stochastic programs we show that the problem-based approach to optimal scenario generation can be reformulated as best approximation problem for the expected recourse function which in turn can be rewritten as a generalized semi-infinite program. We show that the latter is convex if either right-hand sides or costs are random and can be transformed into a semi-infinite program in a number of cases. We also consider problem-based optimal scenario reduction for two-stage models and optimal scenario generation for chance constrained programs. Finally, we discuss problem-based scenario generation for the classical newsvendor problem.
In the context of multistage stochastic optimization problems, we propose a hybrid strategy for generalizing to nonlinear decision rules, using machine learning, a finite data set of constrained vector-valued recourse...
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In the context of multistage stochastic optimization problems, we propose a hybrid strategy for generalizing to nonlinear decision rules, using machine learning, a finite data set of constrained vector-valued recourse decisions optimized using scenario-tree techniques from multistage stochastic programming. The decision rules are based on a statistical model inferred from a given scenario-tree solution and are selected by out-of-sample simulation given the true problem. Because the learned rules depend on the given scenario tree, we repeat the procedure for a large number of randomly generated scenario trees and then select the best solution (policy) found for the true problem. The scheme leads to an ex post selection of the scenario tree itself. Numerical tests evaluate the dependence of the approach on the machine learning aspects and show cases where one can obtain near-optimal solutions, starting with a "weak" scenario-tree generator that randomizes the branching structure of the trees.
To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The unce...
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To address the uncertain renewable energy in the day-ahead optimal dispatch of energy and reserve, a multi-stage stochastic programming model is established in this paper to minimize the expected total costs. The uncertainties over the multiple stages are characterized by a scenario tree and the optimal dispatch scheme is cast as a decision tree which guarantees the flexibility to decide the reasonable outputs of generation and the adequate reserves accounting for different realizations of renewable energy. Most importantly, to deal with the "Curse of Dimensionality" of stochastic programming, stochastic dual dynamic programming (SDDP) is employed, which decomposes the original problem into several sub-problems according to the stages. Specifically, the SDDP algorithm performs forward pass and backward pass repeatedly until the convergence criterion is satisfied. At each iteration, the original problem is approximated by creating a linear piecewise function. Besides, an improved convergence criterion is adopted to narrow the optimization gaps. The results on the IEEE 118-bus system and real-life provincial power grid show the effectiveness of the proposed model and method.
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