This paper presents a tutorial on the state-of-the-art software for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are...
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This paper presents a tutorial on the state-of-the-art software for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are classified according to the decomposition alternatives and the types of the variables in the problem. We review the fundamentals of Benders decomposition, dual decomposition and progressive hedging, as well as possible improvements and variants. We also present extensive numerical results to underline the properties and performance of each algorithm using software implementations, including DECIS, FORTSP, PySP, and DSP. Finally, we discuss the strengths and weaknesses of each methodology and propose future research directions.
Due to the new carbon neutral policies, many district heating operators start operating their combined heat and power plants using different types of biomass instead of fossil fuel. The contracts with the biomass supp...
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Due to the new carbon neutral policies, many district heating operators start operating their combined heat and power plants using different types of biomass instead of fossil fuel. The contracts with the biomass suppliers are negotiated months in advance and involve many uncertainties from the energy producer's side. The demand for biomass is uncertain at that time, and heat demand and electricity prices vary drastically during the planning period. Furthermore, the optimal operation of combined heat and power plants has to consider the existing synergies between the power and heating systems. We propose a solution method using stochastic optimization to support the biomass supply planning for combined heat and power plants. Our two-phase approach determines mid-term decisions about biomass supply contracts as well as short-term decisions regarding the optimal production of the producer to ensure profitability and feasibility. We present results based on ten realistic test cases placed in two municipalities.
An accessible and rigorous presentation of contemporary models and ideas of stochastic programming, this book focuses on optimization problems involving uncertain parameters for which stochastic models are available. ...
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ISBN:
(数字)9781611976595
ISBN:
(纸本)9781611976588
An accessible and rigorous presentation of contemporary models and ideas of stochastic programming, this book focuses on optimization problems involving uncertain parameters for which stochastic models are available. Since these problems occur in vast, diverse areas of science and engineering, there is much interest in rigorous ways of formulating, analyzing, and solving them.
This substantially revised edition
presents a modern theory of stochastic programming, including expanded and detailed coverage of sample complexity, risk measures, and distributionally robust optimization;
adds two new chapters that provide readers with a solid understanding of emerging topics;
updates Chapter 6 to now include a detailed discussion of the interchangeability principle for risk measures; and
presents new material on formulation and numerical approaches to solving periodical multistage stochastic programs.
Lectures on stochastic programming: Modeling and Theory, Third Edition is written for researchers and graduate students working on theory and applications of optimization, with the hope that it will encourage them to apply stochastic programming models and undertake further studies of this fascinating and rapidly developing area.
One effective way to compensate for uncertainties is the use and management of energy storage. Therefore, a new method based on stochastic programming (SP) is proposed here, for optimal bidding of a generating company...
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One effective way to compensate for uncertainties is the use and management of energy storage. Therefore, a new method based on stochastic programming (SP) is proposed here, for optimal bidding of a generating company (GenCo) owning a compressed air energy storage (CAES) along with wind and thermal units to maximize profits. This scheduling has been presented for the GenCo's participation in day-ahead energy and spinning reserve (SR) markets and CVaR is also considered as a risk-controlling index. Firstly, the obtained results are validated by comparing with those of two previous studies. Then, the complete results of the proposed method are presented on a real power system, which indicate the capability of SP in scheduling CAES units. Furthermore, it is observed that CAES units can gain greater profits in joint energy and reserve markets due to their high ramp rates. In addition, the value of stochastic solution (VSS) is used to quantify the advantage of the stochastic method over a deterministic one, which illustrates the advantage of SP-based optimal bidding method especially for CAES and wind units and also for risk-averse GenCos. Overall, it is concluded that the stochastic method is efficient for optimal-bidding of GenCos owning CAES and wind units. (C) 2019 Elsevier Ltd. All rights reserved.
In this paper, the optimal operation problem of smart micro-grids integrated with the pricing of Time-of-Use (TOU) demand response (DR) program is modeled as a two-stage stochastic programming problem with the aim of ...
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In this paper, the optimal operation problem of smart micro-grids integrated with the pricing of Time-of-Use (TOU) demand response (DR) program is modeled as a two-stage stochastic programming problem with the aim of minimizing the cost of MG operation and running TOU in the presence of renewable resources and incentive-based DR programs. Here, TOU as the most common type of time-based DR programs is implemented using a linear function based on the concept of self- and cross-price elasticity of load demand. In the presented model, the forecasting errors of generation of renewable resources are modeled by probability density functions. The operator of MG decides on two stages for optimal management of its network;the first stage refers to the operation of base condition of MG and the second one is pertaining to after the realization of different scenarios for generation of renewable resources. The base condition of MG refers to the situation in which the active power productions of renewables are equal to the predicted values. The proposed model is solved by Particle Swarm Optimization algorithm. A typical MG is employed to investigate and analyze the different features of the method. By varying the demand response potential of MG consumers, TOU tariffs are determined, and their impact on the results of energy and reserve cost as well as voltage and load profiles of MG are analyzed. Numerical results show the efficiency of DR in reducing costs as well as covering the uncertainty resulting from renewables.
We consider a two-stage stochastic variational inequality arising from a general convex two-stage stochastic programming problem, where the random variables have continuous distributions. The equivalence between the t...
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We consider a two-stage stochastic variational inequality arising from a general convex two-stage stochastic programming problem, where the random variables have continuous distributions. The equivalence between the two problems is shown under some moderate conditions, and the monotonicity of the two-stage stochastic variational inequality is discussed under additional conditions. We provide a discretization scheme with convergence results and employ the progressive hedging method with double parameterization to solve the discretized stochastic variational inequality. As an application, we show how the water resources management problem under uncertainty can be transformed from a two-stage stochastic programming problem to a two-stage stochastic variational inequality, and how to solve it, using the discretization scheme and the progressive hedging method with double parameterization.
Several methods have been presented in the literature for the management of a pharmaceutical portfolio, i.e. selecting which clinical studies should be conducted. We compare two existing approaches that use stochastic...
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Several methods have been presented in the literature for the management of a pharmaceutical portfolio, i.e. selecting which clinical studies should be conducted. We compare two existing approaches that use stochastic programming techniques and formulate the problem as a mixed integer linear programme (MILP). The first approach will be referred to as the ROV (real option valuation) approach since values are assigned to drug development programmes using methods for real option valuation. The second approach will be referred to as the PS (project scheduling) approach as this approach focusses on the scheduling of clinical studies and is formulated similarly to the resource constrained project scheduling problem. The ROV approach treats the value of a drug development programme as stochastic whereas the PS approach treats the trial outcomes as the stochastic component of the programme. As a consequence, the two approaches may select different portfolios. An advantage of the PS approach is that a schedule for when trials are to be conducted is provided as part of the optimal solution. This advantage comes at a much increased computational burden, however.
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is thatallscenario subproblems have to be solved at each ...
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Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is thatallscenario subproblems have to be solved at each iteration. In this paper, we introduce randomized versions of the Progressive Hedging algorithm able to produce new iterates as soon as asinglescenario subproblem is solved. Building on the relation between Progressive Hedging and monotone operators, we leverage recent results on randomized fixed point methods to derive and analyze the proposed methods. Finally, we release the corresponding code as an easy-to-use Julia toolbox and report computational experiments showing the practical interest of randomized algorithms, notably in a parallel context. Throughout the paper, we pay a special attention to presentation, stressing main ideas, avoiding extra-technicalities, in order to make the randomized methods accessible to a broad audience in the Operations Research community.
In this paper a stochastic districting problem is investigated. Demand is assumed to be represented by a random vector with a given joint probability distribution function. A two-stage mixed-integer stochastic program...
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In this paper a stochastic districting problem is investigated. Demand is assumed to be represented by a random vector with a given joint probability distribution function. A two-stage mixed-integer stochastic programming model is proposed. The first stage comprises the decision about the initial territory design: the districts are defined and all the territory units assigned to one and exactly one of them. In the second stage, i.e., after demand becomes known, balancing requirements are to be met. This is ensured by means of two recourse actions: outsourcing and reassignment of territory units. The objective function accounts for the total expected cost that includes the cost for the first-stage territory design plus the expected cost incurred at the second stage by outsourcing and reassignment. The (re)assignment costs are associated with the distances between territory units, i.e., the focus is put on the compactness of the solution. The model is then extended in different ways to account for aspects of practical relevance such as a maximum desirable dispersion, reallocation constraints, or similarity of the second-stage solution w.r.t. the first-stage one. The new modeling framework proposed is tested computationally using instances built using real geographical data.
We propose an algorithm for solving a class of bi-objective multistage stochastic linear programs. We show that the cost-to-go functions are saddle functions, and we exploit this structure, developing a new variant of...
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We propose an algorithm for solving a class of bi-objective multistage stochastic linear programs. We show that the cost-to-go functions are saddle functions, and we exploit this structure, developing a new variant of the stochastic dual dynamic programming algorithm. Our algorithm is implemented in the open-source stochastic programming solver ***. We apply our algorithm to a hydro-thermal scheduling problem using data from the Brazilian Interconnected Power System. We also propose and implement a computationally tractable heuristic for bi-objective stochastic convex programs.
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