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An inexact two-stage stochastic robust programming for residential micro-grid management-based on random demand

ENERGY 2014年 67卷 186-199页

作者： Ji, L. Niu, D. X. Huang, G. H. North China Elect Power Univ Sch Econ & Management Res Inst Technol Econ Forecasting & Assessment Beijing 102206 Peoples R China Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada

In this paper a stochastic robust optimization problem of residential micro-grid energy management is presented. Combined cooling, heating and electricity technology (CCHP) is introduced to satisfy various energy demands. two-stage programming is utilized to find the optimal installed capacity investment and operation control of CCHP (combined cooling heating and power). Moreover, interval programming and robust stochastic optimization methods are exploited to gain interval robust solutions under different robustness levels which are feasible for uncertain data. The obtained results can help micro-grid managers minimizing the investment and operation cost with lower system failure risk when facing fluctuant energy market and uncertain technology parameters. The different robustness levels reflect the risk preference of micro-grid manager. The proposed approach is applied to residential area energy management in North China. Detailed computational results under different robustness level are presented and analyzed for providing investment decision and operation strategies. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： stochastic robust optimization Interval linear programming two-stage stochastic programming Micro-grid Uncertainty

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Log-barrier method for two-stage quadratic stochastic programming

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APPLIED MATHEMATICS AND COMPUTATION 2005年第1期164卷 45-69页

作者： Cho, GM Dongseo Univ Div Internet Engn Pusan 617716 South Korea

In this paper we present a log-barrier method for solving two-stage quadratic stochastic programs. The mathematical model considered here can be used to present several real world applications, including financial and production planning problems. We discuss fundamental properties associated with the proposed algorithm and analyze the convergence and complexity of the algorithm. (c) 2004 Elsevier Inc. All rights reserved.

关键词： two-stage stochastic programming log-barrier method complexity polynomial algorithm

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Developing a two stage stochastic programming model of the price and lead-time decision problem in the multi-class make-to-order firm

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COMPUTERS & INDUSTRIAL ENGINEERING 2011年第4期61卷 1086-1097页

作者： Chaharsooghi, S. Kamal Honarvar, Mahboobeh Modarres, M. Kamalabadi, Isa Nakhai Tarbiat Modares Univ Dept Ind Engn Sch Engn Tehran Iran Sharif Univ Technol Dept Ind Engn Tehran Iran

Pricing coordination and due-date management are managerial challenges in today's competitive marketplace. Segmenting orders into classes and allocating resources based on their sensitivity to time and price can increase a firm's profit and its capacity utilization. In addition, other parameters such as production policy, inventory holding and delivery system should be considered in pricing and due-date decisions. In this paper, we consider the role of flexibility in price, lead-time and delivery in the make-to-order environment, where limited production capacity under a stochastic demand function is allowed. We develop a two-stage stochastic programming model to determine the price, lead-time and production amount jointly in each period. The difficulty of continuous distributions is avoided by using a scenario-based approach for stochastic demand. Through numerical analyses, we indicate the benefits of flexibility in delivery, price and lead-time in various environments. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Pricing Lead-time Production two-stage stochastic programming

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Risk averse optimal operation of a virtual power plant using two stage stochastic programming

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ENERGY 2014年第0期73卷 958-967页

作者： Tajeddini, Mohammad Amin Rahimi-Kian, Ashkan Soroudi, Alireza Univ Tehran Sch Elect & Comp Engn Smart Network Lab Tehran Iran Univ Coll Dublin Sch Elect Elect & Commun Engn Dublin 2 Ireland

VPP (Virtual Power Plant) is defined as a cluster of energy conversion/storage units which are centrally operated in order to improve the technical and economic performance. This paper addresses the optimal operation of a VPP considering the risk factors affecting its daily operation profits. The optimal operation is modelled in both day ahead and balancing markets as a two-stage stochastic mixed integer linear programming in order to maximize a GenCo (generation companies) expected profit Furthermore, the CVaR (Conditional Value at Risk) is used as a risk measure technique in order to control the risk of low profit scenarios. The uncertain parameters, including the PV power output, wind power output and day-ahead market prices are modelled through scenarios. The proposed model is successfully applied to a real case study to show its applicability and the results are presented and thoroughly discussed. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： VPP two-stage stochastic programming Risk CVaR Scenario based modelling Uncertainty

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Necessary Optimality Conditions for two-stage stochastic programming Problems

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Optimization 1985年第4期16卷 607-616页

作者： Vogel, Silvia Technische Hochschule Ilmenau Sektion Mathematik Rechentechnik und ökonomische Kybernetik Germany

Using the theory of generalized gradients for locally Lipschitz functions, optimality conditions for two-stage problems of stochastic programming with constraints that have to be satisfied almost surely- and constraints in integral form are derived. The distribution of the random variable may depend on the decision of the first stage;it is assumed, however, that there is a σ-finite measure which dominates all probability measures occuring in the Problem. © 1985, Taylor & Francis Group, LLC. All rights reserved.

关键词： Generalized gradients Locally LIPSCHITZ functions Optimality conditions two-stage stochastic programming

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A simulation-based two-stage interval-stochastic programming model for water resources management in Kaidu-Konqi watershed,China

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Journal of Arid Land 2012年第4期4卷 390-398页

作者： Yue HUANG Xi CHEN YongPing LI AnMing BAO YongGang MA College of Urban and Environmental Sciences Peking University Beijing 100871 China StateKey Laboratory of Desert and Oasis Ecology Xinjiang Institute of Ecology and Geography Chinese Academy of Sciences Urumqi 830011 China MOE Key Laboratory of Regional Energy Systems Optimization Sino-Canada Resources and Environmental ResearchAcademy North China Electric Power University Beijing 102206 China Xinjiang Remote Sensing Center Urumqi 830011 China

This study presented a simulation-based two-stage interval-stochastic programming （STIP） model to support water resources management in the Kaidu-Konqi watershed in Northwest China. The modeling system coupled a distributed hydrological model with an interval two-stage stochastic programing （ITSP）. The distributed hydrological model was used for establishing a rainfall-runoff forecast system, while random parameters were pro- vided by the statistical analysis of simulation outcomes water resources management planning in Kaidu-Konqi The developed STIP model was applied to a real case of watershed, where three scenarios with different water re- sources management policies were analyzed. The results indicated that water shortage mainly occurred in agri- culture, ecology and forestry sectors. In comparison, the water demand from municipality, industry and stock- breeding sectors can be satisfied due to their lower consumptions and higher economic values. Different policies for ecological water allocation can result in varied system benefits, and can help to identify desired water allocation plans with a maximum economic benefit and a minimum risk of system disruption under uncertainty.

关键词： optimization two-stage stochastic programming uncertainty water resources management hydrological model Kaidu-Konqi watershed Tarim River Basin

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Coupling two-stage stochastic Robust programming with Improved Export Coefficient for Water Allocation among Industrial Sectors

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WATER 2022年第12期14卷 1947页

作者： Zhao, Hang Tan, Qian Zhang, Shan Zhang, Tong Zhang, Tianyuan Hu, Kejia China Agr Univ Coll Water Resources & Civil Engn Beijing 100083 Peoples R China Guangdong Univ Technol Sch Ecol Environm & Resources Key Lab City Cluster Environm Safety & Green Dev Guangzhou 510006 Peoples R China Southern Marine Sci & Engn Guangdong Lab Guangzho Guangzhou 511458 Peoples R China

Water scarcity and water pollution are essential factors limiting coordinated regional development, especially in water-deprived regions. Industrial restructuring is an effective water management solution to alleviate water scarcity and mitigate water pollution. However, due to widely existing inexact parameter information in the water resource management system, it is challenging to allocate water resources among industrial sectors. To address these problems, an export coefficient coupled with a two-stage stochastic robust programming method (EC-TSRP) was developed through integrating an export coefficient model (ECM), two-stage stochastic programming (TSP) and robust optimization. The proposed EC-TSRP model could effectively deal with the multiple uncertainties expressed as stochastic and the intervals with fluctuation ranges, and enhance the robustness of optimal plans for supporting water resource allocation among industrial sectors under complex uncertainties. It was then applied to Bayan Nur City, in arid north-west China. The optimization alternatives indicate that wheat, sheep and services would be the most sensitive sectors among all industrial sectors, when non-point source (NPS) pollution exports are restricted. In addition, comparing the EC-TSRP results with the deterministic model, the reliability of the system could be improved significantly, while the value of the objective function would be decreased slightly. The simulation results were also compared with the historical data from 2012 to 2016. Although the total revenue of Bayan Nur City would decrease by 1.52%, the pollutant loads of total nitrogen, total phosphorus and chemical oxygen demand (TN, TP and COD) would decrease by 14.5%, 7.75% and 2.07%, respectively, and total water allocation also would decrease from 4.6 billion m(3) to 4.23 billion m(3).

关键词： two-stage stochastic programming robust optimization export coefficient industrial restructuring

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An Adjustable Robust two-stage stochastic Quadric programming and its Solution with Subgradient Algorithms 22

An Adjustable Robust Two-stage Stochastic Quadric Programmin...

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Proceedings of the 6th International Conference on Algorithms, Computing and Systems

作者： Xinshun Ma Qi An Department of Mathematics and Physics North China Electric Power University China

ISBN: (纸本)9781450397407

Robust stochastic optimization provides a worst-case decision-making scheme under uncertain probability distributions, but the results could be too conservative and pessimistic. This paper establishes a class of adjustable robust two-stage stochastic quadratic programming based on a parameter-related affine uncertain set. The convexity of the problem is verified, and the subdifferential is obtained. An improved subgradient algorithm is proposed for solving the problem based on a deflected subgradient direction and a step-size strategy with exponential decay. The convergence of the algorithm is proved, and the numerical examples demonstrate the effectiveness. The calculation results show that the adjustable robust stochastic programming is related to the parameter-related, and the optima value decreases as the parameter increases. The approach can provide decision-makers with more optimistic solutions besides the worst-case ones.

关键词： Subgradient algorithm Robust stochastic programming two-stage stochastic programming Linear partial information

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Optimizing water use efficiency in industrial parks under uncertainty: An inexact two-stage stochastic partial fractional programming method

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JOURNAL OF WATER PROCESS ENGINEERING 2025年 71卷

作者： Wang, Shuping Lan, Zhuoling Tan, Qian Zhang, Tianyuan Cao, Yini Jiangxi Normal Univ Key Lab Poyang Lake Wetland & Watershed Res Minist Educ Nanchang 330022 Peoples R China Guangdong Univ Technol Guangdong Basic Res Ctr Excellence Ecol Secur & Gr Sch Ecol Environm & Resources Guangdong Prov Key Lab Water Qual Improvement & Ec Guangzhou 510006 Peoples R China Jiangxi Normal Univ Sch Geog & Environm Nanchang 330022 Peoples R China Cent South Univ Forestry & Technol Coll Mat Sci & Engn Changsha 410004 Peoples R China

Optimizing water use efficiency in industrial parks under uncertainty is essential for improving economic development and alleviating water crises. However, previous industrial park water allocation models struggled to manage inflow probability uncertainties and tackle ratio objectives, hindering the improvements of water use efficiency. To address these problems, an inexact two-stage stochastic partial fractional programming (ITSPFP) method was developed for industrial park water management. This method integrates two-stage stochastic programming (TSP) and linear partial information (LPI) within a fractional programming (FP) framework. The ITSPFP method improves upon traditional inexact FP methods by effectively addressing the partial probability distribution of water inflows with the LPI method. ITSPFP also outperforms traditional industrial park water allocation models by optimizing the ratio objective related to water use efficiency and reflecting the penalties associated with water shortages using TSP. ITSPFP was utilized in a case study in Tianjin, China, to illustrate its effectiveness. By maximizing water use efficiency, ITSPFP generated multi-period water allocation plans for industrial parks under varying inflow probabilities. The results showed that higher probabilities of high inflow levels led to reduced water shortages and reclaimed water, while increasing the allocation of surface water and groundwater. Based on the benefits and penalties, prioritizing water supply for the electric power plant is recommended. Compared to the maximum-benefit models, ITSPFP can enhance water use efficiency by [4.03, 9.51]% and reduce water use by [26.80, 39.01]%. By handling uncertain probabilities, ITSPFP also exceeds previous models in avoiding missed potential solutions and enabling greater flexibility in decision making.

关键词： two-stage stochastic programming Linear partial information Uncertainty Fractional programming Industrial park water management

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End-of-life vehicles allocation management under multiple uncertainties: An interval-parameter two-stage stochastic full-infinite programming approach

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RESOURCES CONSERVATION AND RECYCLING 2016年第0期114卷 1-17页

作者： Simic, Vladimir Univ Belgrade Fac Transport & Traff Engn Vojvode Stepe 305 Belgrade 11000 Serbia

One of the main negative consequences of uncontrolled export of used vehicles from the European Union to developing countries is resource shortage for major players of European vehicle recycling systems. The resource scarcity puts serious pressure on vehicle recycling managers. An effective end-of-life vehicles (ELVs) allocation management is considered vital for mitigating the effect of the growing export of used vehicles. This paper proposes an interval-parameter two-stage stochastic full-infinite programming model for end-of-life vehicles allocation management under multiple uncertainties. A case study is conducted in order to demonstrate the potentials and applicability of the proposed model. Influences of parameter uncertainty on model solutions are thoroughly investigated. The developed model can efficiently handle uncertainties expressed as functional intervals, probability distributions and conventional crisp intervals. It is able to reduce risk of ELV management system failure due to the possible constraints violation. The formulated model can take into account connections of modeling parameters and their impact factors, thus reflecting external uncertainties of ELV management systems. It can provide a flexible ELV allocation management schemes adjustable with the variations in prices of secondary metals and end-of-life vehicles. The proposed model is able to reflect trade-off between conflicting waste management system revenues and the associated penalties for violating ELV allocation targets, thus providing a valuable insight for decision makers. (C) 2016 Elsevier B.V. All rights reserved.

关键词： End-of-life vehicle Full-infinite programming two-stage stochastic programming Interval programming Uncertainty

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