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A NEW UNCERTAIN TWO-STAGE NETWORK DEA MODEL BASED ON chance-constrained programming

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2025年第3期21卷 2032-2051页

作者： Yang, Sijia Yangu, Xiangfeng Univ Int Business & Econ Sch Informat Technol & Management Beijing 100029 Peoples R China

This study examines the transformation of DEA models in the presence of data inaccuracies and focuses on the supplier selection problem in sustainable supply chain management. When it comes to green or sustainable fields, environmental and social elements frequently struggle with data imprecision issues. To overcome this difficulty, this paper introduces uncertainty theory and chance-constrained programming and establishes an uncertain two-stage network DEA model. It is assumed that there are several sub-stages in performance evaluation, which can help us identify effective stages of suppliers and make supplier selection more targeted. A numerical example is presented to demonstrate the evaluation process for uncertain data. Finally, our model is applied to the welding supply chain, and it has been proven to be effective by comparing it with data source article models.

关键词： Uncertainty theory chance-constrained programming data envelopment analysis supplier selection

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A copula-based chance-constrained programming framework for BMPs spatial configuration planning

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JOURNAL OF HYDROLOGY 2025年 659卷

作者： Ding, Wenlu Xia, Jun Huang, Sheng Sun, Lanxin Wuhan Univ State Key Lab Water Resources & Hydropower Engn Sc Wuhan 430072 Peoples R China Chinese Acad Sci Inst Geog Sci & Nat Resources Res Key Lab Cycle & Related Land Surface Proc Beijing 100101 Peoples R China

Optimizing spatial pattern of best management practices (BMPs) is crucial for managing non-point source pollution at the watershed scale. However, uncertainties of BMPs effects caused by variant hydro-meteorological conditions can pose challenges to achieving water quality management goals, emphasizing the need to incorporate these uncertainties into decision-making. This study established a credibility chance-constrained programming (CCP) framework that incorporates multiple techniques, including uncertainty modelling, stochastic simulation-optimization technique, clustering and fuzzy set theory. Correlated uncertainties of BMPs effects were described by vine copulas and propagated to the watershed outlet via a Markov-based surrogate model. Fast non-dominated sorting genetic algorithm (NSGA-II), was adopted to optimize cost and pollutant reduction goals while quantifying the reliability of each solution. The developed framework can provide the best compromising solutions (BCSs) among numerous solutions generated by NSGA-II. A case study was conducted to manage Total Nitrogen (TN) and Total Phosphorus (TP) pollution in the upper Boyang River watershed, China. The results show that the system cost increased by up to 3.4 times with the increase of reduction goal (30-60%). Specially, higher credibility levels allow for slight increases in pollution loads (1.48%-5.67%) without significantly raising costs. Overall, by incorporating uncertainty into pollutant reduction scenarios, the framework enables decision-makers to balance costs and environmental benefits while ensuring robust and reliable decisions. This approach is highly adaptable to BMP planning in complex environmental systems, enhancing its practicality for multi-objective watershed management.

关键词： Non-point source pollution BMPs-related decision-making Vine Copulas Uncertainty chance-constrained programming Multi-objective evolutionary algorithm

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chance-constrained programming Models and Approximations for General Stochastic Bottleneck Spanning Tree Problems

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INFORMS JOURNAL ON COMPUTING 2015年第2期27卷 301-316页

作者： Shen, Siqian Kurt, Murat Wang, Jue Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA SUNY Buffalo Dept Ind & Syst Engn Buffalo NY 14260 USA

We consider a balance-constrained stochastic bottleneck spanning tree problem (BCSBSTP) where edge weights are independently distributed but may follow arbitrary continuous distributions. The goal is to minimize a threshold variable that may be exceeded by the maximum edge weight at certain risk, subject to the minimum edge weight being no less than a fixed threshold with a probability guarantee. We characterize these two requirements as chance constraints, which are typically used for bounding the risk of undesirable random outcomes. Given independently distributed edge weights, we reformulate BCSBSTP as a mixed-integer nonlinear program, approximated by two mixed-integer linear programs based on special ordered set of type one (SOS1) and special ordered set of type two (SOS2) variables. By relaxing the probabilistic guarantee on the minimum edge weight in BCSBSTP, we also consider a stochastic bottleneck spanning tree problem (SBSTP), of which optimal tree solutions are approximated via a bisection algorithm in pseudopolynomial time. We demonstrate computational results of our models and algorithms by testing randomly generated instances with edge weights following a diverse set of independent distributions.

关键词： stochastic bottleneck spanning tree chance-constrained programming special ordered sets bisection algorithm NP-complete

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chance-constrained programming Method of IT Risk Countermeasures for Social Consensus Making

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2015年第5期45卷 725-733页

作者： Samejima, Masaki Sasaki, Ryoichi Osaka Univ Grad Sch Informat Sci & Technol Dept Multimedia Engn Suita Osaka 5650871 Japan Tokyo Denki Univ Sch Sci & Technol Future Life Tokyo 1208551 Japan

The authors address a social consensus making support in discussing countermeasures for information technology risks (IT risks). For supporting stakeholders' discussion on which IT risk countermeasures the stakeholders should implement, experts of the risk management estimate parameter values of the countermeasure, define a goal and constraints, and formulate the decision problem of the countermeasures to be implemented as one of 0-1 integer programming problems. Because parameter values and constraint values are uncertain, the decision problem is reformulated as a chance-constrained programming problem. The sample average approximation method is a well-known method for solving the chance-constrained programming problem. However, the computational time is still so long that the opinion leaders cannot use a solution of the chance-constrained programming problem in their discussion. The authors propose a high-speed chance-constrained programming method by aggregating the constraints that are generated by approximation of the problem in the sample average method. By applying the proposed method to real decision problems, the authors confirmed that computational time is decreased to 1 min while obtaining the same error rate and the same rate of the feasible solutions as a conventional method.

关键词： chance-constrained programming constraint aggregation information technology risk (IT risk) sample average approximation method social consensus making

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chance-constrained programming for day-ahead scheduling of variable wind power amongst conventional generation mix and energy storage

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IET RENEWABLE POWER GENERATION 2017年第14期11卷 1785-1793页

作者： Tan, Wen-Shan Shaaban, Mohamed Abdullah, Md Pauzi Univ Teknol Malaysia Inst Future Energy CEES Fac Elect Engn Johor Baharu 81310 Johor Malaysia Univ Malaysia Sarawak Dept Elect & Elect Engn Fac Engn Kota Samarahan 94300 Sarawak Malaysia Port Said Univ Dept Elect Engn Fac Engn Port Fouad 42523 Port Said Egypt

This study presents a day-ahead scheduling of a generation portfolio incorporating large shares of intermittent wind generation. The scheduling utilises the cycling of conventional generation as well as the dispatch of energy storage (ES) to mitigate the impact of net load ramps. Inherent system flexibility, expressed as a chance constraint, is quantified in terms of ramping capability and operating reserves of conventional generation and ES. The flexibility chance constraint is then factorised into a set of linear deterministic inequalities, to preserve the mixed-integer linear programming structure of the resulting problem. Numerical simulations are performed and results are analysed for IEEE 24-bus and 118-bus systems. Test results show that implementation of ES improves the flexibility of the system, in terms of alleviation of the cycling of thermal generation as well as wind generation curtailment.

关键词： power generation scheduling power generation dispatch wind power integer programming linear programming power generation economics investment chance-constrained programming day-ahead scheduling variable wind power conventional generation mix and energy storage dispatch generation portfolio intermittent wind generation net load ramp impact mitigation flexibility chance constraint linear deterministic inequalities mixed-integer linear programming structure IEEE 24-bus system IEEE 118-bus system thermal generation cycling wind generation curtailment

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chance-constrained programming models for capital budgeting with NPV as fuzzy parameters

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2007年第1期198卷 149-159页

作者： Huang, Xiaoxia Univ Sci & Technol Beijing Sch Management Beijing 100083 Peoples R China

In an uncertain economic environment, experts' knowledge about outlays and cash inflows of available projects consists of much vagueness instead of randomness. Investment outlays and annual net cash flows of a project are usually predicted by using experts' knowledge. Fuzzy variables can overcome the difficulties in predicting these parameters. In this paper, capital budgeting problem with fuzzy investment outlays and fuzzy annual net cash flows is studied based on credibility measure. Net present value (NPV) method is employed, and two fuzzy chance-constrained programming models for capital budgeting problem are provided. A fuzzy simulation-based genetic algorithm is provided for solving the proposed model problems. Two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the proposed algorithm. (c) 2005 Elsevier B.V. All rights reserved.

关键词： capital budgeting fuzzy programming chance-constrained programming NPV

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chance-constrained programming in activity networks: A critical evaluation

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第2期131卷 440-458页

作者： Elmaghraby, SE Soewandi, H Yao, MJ N Carolina State Univ Coll Engn Dept Ind Engn Raleigh NC 27695 USA N Carolina State Univ Coll Engn Grad Program Operat Res Raleigh NC 27695 USA Microstrategy Incorp Vienna VA 22182 USA Tunghai Univ Dept Ind Engn Taichung 407 Taiwan

We review the chance-constrained programming (CCP) model for event realization in activity networks (ANs), and the more recent contribution to it by Kress, from the points of view of validity and accuracy. We present a classification scheme of stochastic programming and confirm that the CCP does not solve the problem of finding a point estimate that satisfies a required confidence level, and is of little help in determining the cumulative distribution function (c,d.f,) of the project completion time. We show that the CCP leads to an extremely weak lower bound (I.b.) on the exact c.d.f. A backtracking approach is proposed that improves this l.b. via the CCP, which is still too weak to be of any practical value. Finally, we utilize the CCP approach to derive a result due to Kress in a simpler and more direct way. We also demonstrate that the result itself. unfortunately, is of questionable validity. (C) 2001 Elsevier Science B,V, Ah rights reserved.

关键词： activity networks chance-constrained programming

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chance-constrained programming Method by Constraints Aggregation for Social Consensus Making on IT Risk Countermeasure

Chance-constrained Programming Method by Constraints Aggrega...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Sato, Katsunori Samejima, Masaki Sasaki, Ryoichi Osaka Univ Grad Sch Informat Sci & Technol 2-1 Yamadaoka Suita Osaka Japan Tokyo Denki Univ Sch Sci & Technol Future Life Tokyo 1208551 Japan

ISBN: (纸本)9781479906529

This paper addresses the chance-constrained programming for the social consensus making on IT risk counter-measures. The sample average approximation method is a well-known method for solving the chance-constrained programming. However, the computational time is still so long that the opinion leaders can not use the solution of the chance-constrained programming in their discussion. So, we proposed the interactive chance-constrained programming method to show the solutions that are being searched to the opinion leaders. Through the preliminary experiment, we clarified the issues of sampling for the approximation and controlling the search of the solution.

关键词： chance-constrained programming

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chance-constrained programming : a Tool for Solving Linear Eddy Current Inverse Problem

Chance-Constrained Programming : a Tool for Solving Linear E...

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13th International Workshop on Electromagnetic Nondestructive Evaluation (ENDE)

作者： Zorgati, Riadh Duchene, Bernard Univ Paris 11 Dept Rech Electromagnetisme Lab Signaux & Syst CNRSSupelec 3 Rue Joliot Curie F-91192 Gif Sur Yvette France EDF R&D Paris France

ISBN: (纸本)9781607504429;9781607500230

This paper deals with the application of chance-constrained programming to eddy current inverse problems, linearized in the Born approximation framework. It suggests two probabilistic formulations of this linear inverse problem: the first one uses joint chance constraints and the second one is based upon individual chance constraints;the latter allows a layer-by-layer reconstruction suitable for taking attenuation into account. The paper illustrates how structural properties of chance constraints are a powerful tool for dealing with the ill-posed nature of the problem. Two situations are considered: i) the first one concerns a flaw made of a simple conductivity contrast and an underlying random process belonging to the class of elliptically symmetric distributions;in that case, a deterministic equivalence of the problem can be found provided that a suitable level of probability is chosen, ii) the second situation concerns a notch;a tractable approximate algorithm based upon the Hoeffding inequality is suggested for solving the inverse problem in that case.

关键词： Eddy Current Linear Inverse Problem chance-constrained programming

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chance-constrained programming (CCP)abatement of SO_2 emission for acid deposition control in Liuzhou City

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Journal of Environmental Sciences 1990年第3期2卷 35-49页

作者： Hao Jiming, Li Guang, Zhang Yang, Xu Kangfn, Ban Ling, Wen Weimin, Yang Jinlan and Liu NingDepartment of Environmental Engineering,Tsinghua Unviersity,Beijing 100084,ChinaResearch Center for Eco-Environmental Sciences,Academis Sinica,Beijing 100083,ChinaResearch Institute for Environmental Sciences of Guangxi-Zhuang Autonomous Region,nanning 530022,ChinaLiuzhou EPA,guangxi-Zhuang Autonomous Region,Liuzhou 545007,China

A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncertainty in the source-receptor-specific transfer coefficients. Based on the calculation of SO2 and sulfate average residence time for Liuzhou City, a sulfur deposition model has been developed and the distribution of transfer coefficients have been found to be approximately log-normal. Sulfur removal minimization of the model shows that the abatement of emission sources in the city is more effective, while control cost optimization provides the lowest cost programmes for source abatement at each allowable deposition limit under varied environmental risk levels. Finally a practicable programme is recommended.

关键词： chance-constrained programming emission source abatement acid deposition.

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