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Optimizing financial and physical assets with chance-constrained programming in the electrical industry

OPTIMIZATION AND ENGINEERING 2011年第1-2期12卷 237-255页

作者： Zorgati, Riadh van Ackooij, Wim EDF R&D OSIRIS 1 F-92141 Clamart France

This paper deals with a chance-constrained programming formulation and approximate resolution of an offer-demand equilibrium problem in the context of electricity markets. First, we state the probabilistic model. Computing the coefficients of the problem matrix is easy for financial assets, but a challenging task for physical assets. By introducing maximal production capacities, the computation becomes tractable for thermal plants but still leads to a combinatorial problem for hydraulic production. The obtained problem matrix is sparse, large scale and with random coefficients describing underlying uncertainty factors affecting the available power of assets. Second, we suggest some ways for approximately solving the obtained combinatorial chance-constrained program, which is in fact a stochastic multi-knapsack problem. A formal link between joint and individual chance constraints is exhibited and may lead to a simplified processing of the problem. Finally we illustrate our approximate algorithm on a stylized example.

关键词： Unit commitment Hedging chance-constrained programming

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A joint chance-constrained programming approach for the single-item capacitated lot-sizing problem with stochastic demand

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ANNALS OF OPERATIONS RESEARCH 2018年第1-2期264卷 123-155页

作者： Gicquel, Celine Cheng, Jianqiang Univ Paris Sud Lab Rech Informat Paris France Univ Arizona Dept Syst & Ind Engn Tucson AZ 85721 USA

We study the single-item single-resource capacitated lot-sizing problem with stochastic demand. We propose to formulate this stochastic optimization problem as a joint chance-constrained program in which the probability that an inventory shortage occurs during the planning horizon is limited to a maximum acceptable risk level. We investigate the development of a new approximate solution method which can be seen as an extension of the previously published sample approximation approach. The proposed method relies on a Monte Carlo sampling of the random variables representing the demand in all planning periods except the first one. Provided there is no dependence between the demand in the first period and the demand in the later periods, this partial sampling results in the formulation of a chance-constrained program featuring a series of joint chance constraints. Each of these constraints involves a single random variable and defines a feasible set for which a conservative convex approximation can be quite easily built. Contrary to the sample approximation approach, the partial sample approximation leads to the formulation of a deterministic mixed-integer linear problem having the same number of binary variables as the original stochastic problem. Our computational results show that the proposed method is more efficient at finding feasible solutions of the original stochastic problem than the sample approximation method and that these solutions are less costly than the ones provided by the Bonferroni conservative approximation. Moreover, the computation time is significantly shorter than the one needed for the sample approximation method.

关键词： Stochastic lot-sizing chance-constrained programming Joint probabilistic constraint Sample approximation approach Mixed-integer linear programming

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A chance-constrained programming Approach to the Design of Robust Broadband Beamformers With Microphone Mismatches

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IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2018年第12期26卷 2475-2488页

作者： Bao, Yu Chen, Huawei Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing 210016 Jiangsu Peoples R China

This paper addresses the design of robust broadband beamformers by taking into account the prior knowledge of uncertain means and variances of microphone mismatches. A chance-constrained programming (CCP) based design approach is proposed, which is a generic extension of the existing worst case mean performance optimization (WMPO) based counterpart by using a chance-constrained stopband level constraint instead of a hard one. The original CCP-based design problem, however, is NP-hard to solve. To deal with the problem, a relaxed convex optimization formulation is developed by exploiting the distribution property of array response distortion due to microphone mismatches. The relation between the proposed CCP- and WMPO-based design approaches is analyzed theoretically. It shows that there always exists a chance constraint probability under which the CCP-based design is comparable to the WMPO-based one, which provides an insight into the overconservatism problem in the WMPO-based design from the perspective of the CCP-based framework. Moreover, a criterion on the setting of the chance constraint probability is also derived for the proposed design approach in order to remedy the overconservatism problem. Simulation and real experimental results are presented to show the superior performance of the proposed design approach compared with its state-of-the-art counterparts.

关键词： Broadband beamformers microphone arrays microphone mismatches robustness chance-constrained programming worst-case mean performance optimization

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chance-constrained programming and robust optimization approaches for uncertain hub location problems in a cooperative competitive environment

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SCIENTIA IRANICA 2022年第4期29卷 2149-2165页

作者： Nourzadeh, F. Ebrahimnejad, S. Khalili-Damghani, K. Hafezalkotob, A. Islamic Azad Univ Dept Ind Engn South Tehran Branch Tehran Iran Islamic Azad Univ Dept Ind Engn Karaj Branch POB 8485-313 Karaj Iran

In this paper, an integer programming model is offered for capacitated multial-location median hub location problems applicable to both cooperative and competitive environments among airlines. We divided the hubs into six independent categories by comparing the parameters of ticket price, travel time, and service quality for both the follower and leader airlines. The degrees of importance for the parameters of time and cost were determined by a multivariate Lagrange interpolation method, which could be of significant help in allocating travelers to the follower airline hubs. Then, with regard to the seasonal demand of travelers, travel demand was considered as an uncertain parameter. To identify the deterministic equivalent forms for the considered categories of hub location models, the robust optimization method and the chance-constrained programming model were employed. Finally, the developed model was tested for a case study. The results indicated that the coalition of follower airlines could absorb nearly 2% of the leader airline travelers with relatively lower travel cost and time. (C) 2022 Sharif University of Technology. All rights reserved.

关键词： Hub location problem Robust optimization chance-constrained programming Cooperative competitive environment Multivariate Lagrange interpolation function

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Note on "A chance-constrained programming framework to handle uncertainties in radiation therapy treatment planning"

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第2期275卷 793-794页

作者： Custodio, Janiele Lejeune, Miguel Zavaleta, Antonio George Washington Univ Dept Engn Management & Syst Engn 800 22nd St NW Washington DC 20052 USA George Washington Univ Decis Sci Dept 2201 G St NW Suite 406 Washington DC 20052 USA

A recent article by Zaghian et al. (2018) proposed reformulations, proposed reformulations of stochastic chance-constrained programming models for radiation therapy treatment planning. This note questions the validity of the proposed reformulations and shows that they are not equivalent to the original formulations. Two numerical examples illustrate that the approach proposed by Zaghian et al. (2018) provides approximation problems and not reformulations. Published by Elsevier B.V.

关键词： OR in health services chance-constrained programming Monotonic transformation Reformulation

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chance-constrained programming for optimal scheduling of combined cooling, heating, and power-based microgrid coupled with flexible technologies

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SUSTAINABLE CITIES AND SOCIETY 2022年第0期77卷 103502-103502页

作者： Mianaei, Peyman Khorshidian Aliahmadi, Mohammad Faghri, Safura Ensaf, Mohammad Ghasemi, Amir Abdoos, Ali Akbar Babol Noshirvani Univ Technol Dept Elect & Comp Engn Babol Iran Sharif Univ Technol Ctr Excellence Energy Convers CEEC Sch Mech Engn Azadi AvePOB 11365-9567 Tehran Iran Islamic Azad Univ Elect & Comp Engn Dept Sci & Res Branch Tehran Iran Sharif Univ Technol Dept Chem & Petr Engn Tehran Iran Univ Tehran Sch Environm Coll Engn Tehran Iran

Microgrids (MGs) have a special role in developing several consumers' energy infrastructure and supply in more economical, safer, and sustainable ways. The interaction and mutual relationship between each energy carrier on the reliable performance of other carriers and the high growth of tri-generation technologies in the MG face the optimal performance of such networks with many challenges. Combined cooling, heating, and power (CCHP)-based MGs are a new generation of MGs that simultaneously provide electrical, thermal, and cooling loads. However, the interaction between these carriers is very influential in CCHP-based MG's operation, which is rarely analyzed. Hence, this paper focuses on the operation of CCHP-based MG coupled with hybrid chiller, multi-energy storage, solar and wind power, etc., under the chance-constrained programming (CCP) approach by considering the mutual relationship between carriers. While modeling consumption and wind and solar energies fluctuations, the proposed approach analyzes the violation of the balance constraint for each carrier and subject it to guarantee the corresponding confidence level. Therefore, the degree of dependence of the system on each carrier and the mutual relationship between carriers are analyzed in this work. This paper also presents a new incentive framework for participating in the electricity and heating markets for the system. The proposed model is implemented on the test system, and the results are discussed for different cases for several confidence levels. The results illustrate the importance of the electricity carrier confidence level on the safe performance of the whole system compared to other carriers. Only by increasing the operation cost of the electricity sector by 4.3%, the system's reliable performance is guaranteed with a probability of 98%.

关键词： chance-constrained programming Combined cooling heating and power-based microgrid Confidence level Multi-energy storage Multi-carrier market

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Stochastic transitions of a mixed-integer linear programming model for the construction supply chain: chance-constrained programming and two-stage programming

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OPERATIONAL RESEARCH 2024年第3期24卷 46页

作者： Koutsokosta, Aspasia Katsavounis, Stefanos Democritus Univ Thrace Dept Prod & Management Engn Xanthi Greece

This paper addresses the problem of optimal Construction Supply Chain (CSC) design and integration in deterministic and stochastic environments by providing a family of models for the optimization of a dynamic, multi-product, multi-site contractor-led CSC. With the objective of minimizing the total CSC cost, optimal decisions are made on network design, production, inventory holding and transportation, while also considering discounts for bulk purchases, logistics centers, on-site shortages and an inventory-preparation phase. The models integrate the operations of temporal and project-based supply chains into a sustainable network with repetitive flows, large scope contracts and economies of scale to provide the main contractor with a versatile optimization framework which can account for different levels of uncertainty. The novelty of this paper lies in providing a flexible integrative optimization CSC tool that accounts for multiple CSC actors (suppliers and/or logistics centers), projects, products, time periods, operations, and different decision-making environments depending on the nature of the problem and the risk-attitude of the decision maker. This paper contributes to the fast-growing research field of stochastic CSC optimization showcasing stochastic transitions of a mixed-integer linear programming model to chance-constrained programming and two-stage programming and incorporating uncertainties with different types of probability distributions or scenarios, and even interdependent uncertainties-approaches that have not been explored extensively in the CSC context. The results reveal that the stochastic approaches sacrifice the minimum cost of deterministic solutions having average settings to obtain robust well-hedged solutions over the possible parameter variations and that the selection of a suitable method for modeling uncertainty is context-dependent.

关键词： Construction supply chain management Construction supply chain network design and integration Stochastic optimization Mixed-integer linear programming chance-constrained programming Two-stage programming

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A JOINT chance-constrained programming-MODEL WITH ROW DEPENDENCE

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1994年第2期77卷 325-343页

作者： WATANABE, T ELLIS, H JOHNS HOPKINS UNIV DEPT GEOG & ENVIRONM ENGNBALTIMOREMD 21218

Joint chance-constrained stochastic programming models typically require random row vector independence. A joint model is developed that incorporates not only within-constraint covariance as is usually the case, but also admits dependence between constraints, that is, row dependence. The objective function of the associated chance-constrained deterministic equivalent is a multivariate normal distribution with dimension equal to the number of chance constraints in the original problem. We discuss methods to solve this multinormal integral and evaluate its derivatives. The model is implemented in portable Fortran and applied to two 9-D test problems.

关键词： STOCHASTIC programming chance-constrained programming JOINT chance CONSTRAINTS NONLINEAR OPTIMIZATION MULTINORMAL INTEGRATION

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A chance-constrained programming Model for the Optimal Stopping Decision of Power R&D Project

A Chance-constrained Programming Model for the Optimal Stopp...

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International Conference on Advances in Energy and Environmental Science (ICAEES)

作者： Yi, Changsheng Guan, Xuebin Gao, Jianbing Anhui Univ Technol Sch Management Sci & Engn Maanshan 243032 Anhui Peoples R China

ISBN: (纸本)9783037858615

A power R&D process can be regarded as a jump process of scientific knowledge full of exploration and complexity. Every jump represents a scientific breakthrough or a new discovery in this setting. In this paper, the inter-arrival times are treated as random variables observe arbitrary distributions. The a-optimistic net return of project performance is proposed and a chance-constrained programming model is established to model the power R&D optimal stopping decision problem. Considering the complexity of the model, the stochastic simulation is designed to estimate the values of project return performance and the simultaneous perturbation stochastic approximation (SPSA) algorithm is employed to solve the proposed model. Finally, the effectiveness of the hybrid algorithm and the applicability of the model are illustrated by numerical examples.

关键词： Power R&D project Optimal stopping chance-constrained programming SPSA

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Optimal Dispatch Based on chance-constrained programming 10

Optimal Dispatch Based on Chance-constrained Programming

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IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC)

作者： Zeng, Kaiwen Pan, Mengqi Li, Bo Liu, Jianing Wang, Qi Guo, Yufeng Guangdong Power Grid Power Dispatch Control Ctr Guangzhou Guangdong Peoples R China Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China Harbin Inst Technol Sch Elect Engn & Automat Harbin Peoples R China

ISBN: (纸本)9781538656860

Because of wind turbulent fluctuation, it is difficult to predict wind power fluctuation, which brings problems of randomness and uncertainty to power system stability. This study introduces a method to analyze wind power fluctuation characteristics. An optimal dispatch model-based on chance-constrained programming is established. The function formula of the wind power fluctuation is included in the power balance constraint. Finally, a genetic algorithm is proposed for the model solution, and the economic costs are calculated from this model. The algorithm is consistent with traditional ones and the models proposed in this study are shown to be reasonable and effective.

关键词： power system wind turbulent fluctuation wind power fluctuation chance-constrained programming optimal dispatch

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