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

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

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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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Distributionally robust joint chance-constrained programming with Wasserstein metric

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OPTIMIZATION METHODS & SOFTWARE 2024年第1期40卷 134-168页

作者： Gu, Yining Wang, Yanjun Shanghai Univ Finance & Econ Sch Math Shanghai Peoples R China

In this paper, we develop an exact reformulation and a deterministic approximation for distributionally robust joint chance-constrained programmings (DRCCPs) with a general class of convex uncertain constraints under data-driven Wasserstein ambiguity sets. It is known that robust chance constraints can be conservatively approximated by worst-case conditional value-at-risk (CVaR) constraints. It is shown that the proposed worst-case CVaR approximation model can be reformulated as an optimization problem involving biconvex constraints for joint DRCCP. This approximation is essentially exact under certain conditions. We derive a convex relaxation of this approximation model by constructing new decision variables which allows us to eliminate biconvex terms. Specifically, when the constraint function is affine in both the decision variable and the uncertainty, the resulting approximation model is equivalent to a tractable mixed-integer convex reformulation for joint binary DRCCP. Numerical results illustrate the computational effectiveness and superiority of the proposed formulations.

关键词： Distributionally robust optimization problem chance-constrained programming Wasserstein metric conic optimization mixed-integer programming

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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 NOVEL SEPARATE chance-constrained programming MODEL TO DESIGN A SUSTAINABLE MEDICAL VENTILATOR SUPPLY CHAIN NETWORK DURING THE COVID-19 PANDEMIC

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第2期19卷 1395-1425页

作者： Abad, Amin Reza Kalantari Khalil Barzinpour, Farnaz Pasandideh, Seyed Hamid Reza Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Kharazmi Univ Fac Engn Dept Ind Engn Tehran Iran

Providing new models or designing sustainable networks in recent studies represents a growing trend. However, there is still a gap in the simultaneous modeling of the three dimensions of sustainability in the electronic medical device supply chain (SC). In this paper, a novel hybrid chance-constrained programming and cost function model is presented for a green and sustainable closed-loop medical ventilator SC network design. To bring the problem closer to reality, a wide range of parameters including all cost parameters, demands, the upper bound of the released co2, and the minimum percentage of the units of product to be disposed and collected from a customer and to be dismantled and shipped from DCs are modeled as uncertain along with the normal probability distribution. The problem was first formulated into the framework of a bi-objective stochastic mixed-integer linear programming (MILP) model;then, it was reformulated into a tri-objective deterministic mixed-integer nonlinear programming (MINLP) one. In order to model the environmental sustainability dimension, in addition to handling the total greenhouse gas emissions, the total waste products were also controlled. The efficiency and applicability of the proposed model were tested in an Iranian medical ventilator production and distribution network. For sensitivity analyses, the effect of some critical parameters on the values of the objective functions was carefully examined. Finally, valuable managerial insights into the challenges of companies during the COVID-19 pandemic were presented. Numerical results showed that with the increase in the number of customers in the COVID-19 crisis, social responsibility could improve cost mean by up to 8%.

关键词： Healthcare system sustainable supply chain design closed-loop supply chain ventilator COVID-19 pandemic MINLP optimization chance-constrained programming multi-objective optimization goal attainment

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Energy management for active distribution network incorporating office buildings based on chance-constrained programming

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2022年 134卷 107360-107360页

作者： Su, Su Li, Zening Jin, Xiaolong Yamashita, Koji Xia, Mingchao Chen, Qifang Beijing Jiaotong Univ Natl Act Distribut Network Technol Res Ctr Beijing 100044 Peoples R China Tech Univ Denmark Ctr Elect Power & Energy Elektrovej 325 DK-2800 Lyngby Denmark Univ Calif Riverside Elect & Comp Engn Riverside CA 92521 USA

Aiming to the more flexible operation of the active distribution network (ADN), an energy management method for ADN incorporating office buildings is proposed based on chance-constrained programming. First, based on the thermal dynamics of buildings, an energy consumption prediction model of office buildings with integrated thermostatically controlled loads (TCLs) is developed. Then, an optimal energy management strategy for the ADN is proposed through the branch flow model (BFM) and the second-order cone relaxation (SOCR), considering the constraints of the grid and office buildings. The chance-constrained programming is exploited to consider further the uncertainties of photovoltaic (PV) power and ambient temperature, and the optimization model of the ADN incorporating office buildings is reformulated as a mixed-integer second-order cone programming (MISOCP) problem, using the deterministic transformation of chance constraints. Finally, the impact of the office buildings with TCLs on the economic operation of the ADN is analyzed under different confidence levels in the winter heating scenario. Numerical studies justify that the lower confidence level capitalizes on the thermal storage characteristics of office buildings retaining the temperature comfort of office workers to attain the flexible operation of the ADN additionally.

关键词： Active distribution network (ADN) chance-constrained programming Energy management Office buildings Thermostatically controlled loads (TCLs)

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BESS frequency regulation strategy on the constraints of planned energy arbitrage using chance-constrained programming

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ENERGY REPORTS 2022年 8卷 73-80页

作者： Xie, Rui Wang, Yilin Zhang, Shengqi Lin, Bin Chen, Qing Wang, Fei Wang, Xiaohe Chen, Yuwei Xia, Bingqing Key Lab Far Shore Wind Power Technol Zhejiang Pro Hangzhou Peoples R China Shanghai Univ Sch Mechatronie Engn & Automat Shanghai Peoples R China PowerChina Huadong Engn CO LTD Hangzhou Peoples R China

Battery energy storage systems (BESS) are regarded as a multi-functional power system participator, participating in the energy arbitrage strategy (EAS), the frequency regulation strategy (FRS) and so on. However, the existing BESS mainly make profit from the EAS instead of the FRS in many countries such as China. Because there is no appropriate control strategy for BESS, when the developing ancillary services market cannot price the contribution of BESS in FRS. Meanwhile, BESS do have redundant power and capacity, if only the EAS is applied. Therefore, it is significant that BESS are involved in the FRS, that the EAS has the priority in BESS utilization. In this paper, a frequency regulation strategy for the user-side BESS is proposed, on the constraints of the planned energy arbitrage. Specifically, the chance-constrained programming is applied to solve the randomness of frequency regulation requirement, ensuring the BESS profit from the EAS. Also, the exiting BESS are fully used with extra profit from FRS. At last, the promising results prove the advantages of the proposed FRS. (C) 2022 Published by Elsevier Ltd.

关键词： Battery energy storage system Energy arbitrage Frequency regulation chance-constrained programming

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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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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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Network-level pavement maintenance and rehabilitation planning considering uncertainties using chance-constrained programming

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INTERNATIONAL JOURNAL OF PAVEMENT ENGINEERING 2024年第1期25卷

作者： Cao, Rui Meng, Siyuan Feng, Shengkai Dong, Shi Bai, Qiang Changan Univ Sch Transportat Engn Xian Peoples R China Howond Design Consulting Co Ltd Xian Peoples R China

In practice, given limited funds, to consider multiple strategic goals/objectives that different stakeholders concern, pavement network-level maintenance and rehabilitation (M&R) planning becomes a multi-objective optimisation (MOO) based project selection and budget allocation problem. In an attempt to solve this problem, most agencies established MOO models under the deterministic situation without appropriate consideration of uncertainties. However, ignoring performance uncertainties often leads to unreasonable decisions. To provide more convincing and reliable pavement M&R decisions, this paper proposes a chance-constrained programming (CCP) based MOO method to incorporate performance uncertainties in network-level single period pavement M&R planning. First, a general deterministic MOO model with budget and network performance constraints is established. Then, three commonly-used statistical forms of network-level performance measures are introduced. To incorporate uncertainties, the probability distribution of each form of performance measure is derived. Based on the CCP method, the MOO model is transformed to an equivalent deterministic formulation as a mixed non-linear integer programming (MNLIP) problem. To demonstrate the proposed method, a case study using real data is conducted. The results show that the proposed method can effectively help decision-makers to appropriately incorporate performance uncertainties in conducting network-level pavement M&R planning.

关键词： Pavement management maintenance and rehabilitation multi-objective optimisation network-level performance measures chance-constrained programming

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