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An Improved Solving Approach for interval-Parameter programming and Application to an Optimal Allocation of Irrigation Water Problem

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WATER RESOURCES MANAGEMENT 2016年第2期30卷 701-729页

作者： Yang, Gaiqiang Guo, Ping Li, Mo Fang, Shiqi Zhang, Liudong China Agr Univ Ctr Agr Water Res China Beijing 100083 Peoples R China Taiyuan Univ Sci & Technol Inst Environm Sci Taiyuan 030024 Shanxi Peoples R China Yunnan Agr Univ Coll Water Conservancy & Hydropower & Architectur Kunming 650201 Peoples R China China Agr Univ Coll Water Conservancy & Civil Engn Beijing 100083 Peoples R China

In this study, an improved single-step method (SSM) is developed based on two-step method (TSM) to solve the interval-parameter linear programming (ILP) model of which the right-hand sides are highly uncertain. Two numerical examples are presented to ascertain appropriate value of. in SSM. The risk preference degree of. could be 0.8 for maximum objective function type. To demonstrate the applicability of the developed method, an agricultural water management problem has been provided in the case study section. The results show that SSM is more effective than TSM for complete solutions. There is only partial solution obtained from the first submodel of TSM, because the right-hand side of the wheat output constraint is highly uncertain. Finally, local farmers' net benefit reaches to [8.949, 12.442] x 10(8) RMB (the unit of Chinese currency). The priority order of crops that are needed to be irrigated by surface water is maize > wheat > cotton.

关键词： interval linear programming interval-parameter Single-step method Two-step method Agricultural water management

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A two-stage interval-stochastic programming model for planning end-of-life vehicles allocation under uncertainty

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RESOURCES CONSERVATION AND RECYCLING 2015年 98卷 19-29页

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

The ultimate fate of vehicles can vary, including being recycled, exported, abandoned, illegally treated in unauthorized facilities, stolen and processed for parts or illegally exported, etc. Nowadays, export of used vehicles represents the most significant barrier to the more efficient vehicle recycling in the EU, because millions of vehicles (mainly from Germany, Italy, UK and France), which are expected to go to domestic vehicle recycling factories are exported. As a result, how to allocate limited and frequently insufficient quantities of collected end-of-life vehicles (ELVs) to satisfy vast demands of vehicle recycling factories becomes a significant concern of many government or private authorities that control the ELV collection and treatment networks across the EU. In this paper, a two-stage interval-stochastic programming model is developed for supporting the management of ELV allocation under uncertainty. The formulated model can directly handle uncertainties expressed as either probability density functions or discrete intervals. Moreover, it can support the analysis of various policy scenarios that are associated with different levels of economic penalties when the promised ELV allocation targets are violated. The proposed model has been applied to a hypothetical case study in which several scenarios with different ELV allocation policies were comprehensively analyzed. The obtained results indicated that reasonable solutions had been generated. There is significant influence of parameter uncertainty on model solutions and the analyzed policy scenarios. Various policies in negotiating the ELV allocation targets with vehicle recycling factories would lead to different economic and risk values. Proposed model can serve as the support for authorities to identify ELV allocation targets that will secure maximized profits and minimized disruption risks of the vehicle recycling factories. It is applicable across vehicle recycling industry that processes dozens o

关键词： End-of-life vehicle Decision making Stochastic programming interval linear programming Uncertainty

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An approach to interval programming problems with left-hand-side stochastic coefficients: An application to environmental decisions analysis

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EXPERT SYSTEMS WITH APPLICATIONS 2011年第9期38卷 11538-11546页

作者： Cao, M. F. Huang, G. H. He, L. Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada N China Elect Power Univ Sino Canada Ctr Energy & Environm Res Beijing 102206 Peoples R China Ryerson Univ Dept Civil Engn Ryerson ON M5B 2K3 Canada

An interval programming with stochastic coefficients (IPSC) model is developed for planning of regional air quality management. The IPSC model incorporates stochastic coefficients with multivariate normal distributions within an interval parameter linear programming (ILP) framework. In IPSC, system uncertainties expressed as stochastic coefficients and intervals are addressed. Since stochastic coefficients are the left-hand-side (LHS) parameters of the constraints in IPSC, a left-hand-side chance-constrained programming (LCCP) method is developed to solve the problem. The developed IPSC model is applied to a regional air quality management system. Uncertainties in both abatement efficiencies expressed as stochastic coefficients and environmental standards expressed as intervals are reflected. interval solutions associated with different violation probability levels and/or different environmental standards have been obtained. Air quality managers can thus analyze the solutions with appropriate combinations of the uncertainties and gain insight into the tradeoffs between the abatement costs and the risks of violating different environmental standards. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： interval linear programming Multivariate normal distribution Air quality management Inexact optimization Uncertainty

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Two-stage stochastic programming problems involving interval discrete random variables

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OPSEARCH 2012年第3期49卷 280-298页

作者： Barik, Suresh Biswal, Mahendra Chakravarty, Debashish Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India Indian Inst Technol Dept Min Engn Kharagpur 721302 W Bengal India

In this paper, we propose a two-stage stochastic linear programming problem considering some of the left hand side and right hand side of linear constraints parameters as interval discrete random variables with known probability distribution and rest of the parameters are precisely known. Both the randomness and discrete intervals are simultaneously considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are studied in two-stage stochastic programming. To solve the stated problem, first we remove the randomness from the problem and formulate an equivalent deterministic linear programming model with interval coefficients. Then the deterministic model is solved using the solution procedure of linear programming with interval coefficients. We obtain the upper bound and lower bound of the objective function as the best and the worst value respectively. It highlights the possible risk involved in the decision making process. A numerical example is presented to demonstrate the usefulness of the proposed methodology.

关键词： Stochastic programming Two-stage stochastic programming interval linear programming interval discrete random variables

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An interval programming Approach for an Operational Transportation Planning Problem

An Interval Programming Approach for an Operational Transpor...

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15th International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU)

作者： Borodin, Valeria Bourtembourg, Jean Hnaien, Faicel Labadie, Nacima Univ Technol Troyes LOSI ICD 12 Rue Marie Curie CS 42060 F-10004 Troyes France Agr Cooperat Soc Region Arcis Aube Ind Zone Villette F-10700 Villette Aube France

ISBN: (纸本)9783319087955;9783319087948

This paper deals with an interval programming approach for an operational transportation problem, arising in a typical agricultural cooperative during the crop harvest time. More specifically, an interval programming model with uncertain coefficients occurred in the righth- and side and the objective function is developed for a single-period multi-trip planning of a heterogeneous fleet of vehicles, while satisfying the stochastic seed storage requests, represented as interval numbers. The proposed single-period interval programming model is conceived and implemented for a real life agricultural cooperative case study.

关键词： interval linear programming single-period multi-trip transportation planning problem OR in agriculture

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An interval chance-constrained programming-based optimization model for carbon capture, utilization, and storage system planning

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SCIENCE OF THE TOTAL ENVIRONMENT 2021年 772卷 145560-145560页

作者： Zhai, Mingyang Jia, Haifeng Yin, Dingkun Tsinghua Univ Sch Environm Beijing 100084 Peoples R China

Carbon capture, utilization, and storage (CCUS) are widely regarded as a crucial technological option for industrial large-scale carbon dioxide (CO2) emissions reduction. However, high-cost and uncertainties hinder the widespread application of CCUS technology. In this study, an interval-chance-constrained programming-based optimization model was proposed to address random probability distributions, interval values, complex interactions, and the dynamics of capacity expansion issues. The model was applied to a CCUS project in China. A set of violation probability levels (0.01, 0.05, 0.1, and 0.2) were designed to reflect system costs and risk levels. And then the solutions for system costs, capacity expansion, and operating schemes under four violation probability levels (p(i')) could be generated. The results revealed that the model could ensure the highest reliability and largest CO2 storage under p(i') = 0.01. At this probability level, the amount of CO2 storage would range from 4972.05-5429.75 kilotons per annum (ktpa), the CCUS system cost would be highest at $166.57 million, and the net system benefits would be slightly less at $105.91 million. If policymakers strive to achieve the net system benefits of the project, the highest net system benefits would be achieved under p(i') = 0.05. At this probability level, the net system benefits would increase to $135.45 million, the system cost would reduce to 5138.62 million, but the total amount of CO2 storage would decrease to between 4090.01 and 4653.24 ktpa, which would entail a high risk of system violation. These findings enable policymakers to determine the trade-offs among system reliability, CO2 reduction, and the benefits of the project. The modeling approach can also address interactions among CCUS activities and the dynamics of facility expansion issues as well as help policymakers develop adaptive operational strategies. This study enriches CCUS research through an interval chance-constrained optimization

关键词： Carbon capture, utilization, and storage CO2 compression Enhanced oil recovery interval linear programming Chance-constrained programming Uncertainties

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Agricultural effluent control under uncertainty: An inexact double-sided fuzzy chance-constrained model

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ADVANCES IN WATER RESOURCES 2010年第9期33卷 997-1014页

作者： Xu, Y. Qin, X. S. Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore Nanyang Technol Univ DHI NTU Water & Environm Res Ctr & Educ Hub Singapore 639798 Singapore

An inexact double-sided fuzzy chance-constrained programming (IDFCCP) method was developed in this study and applied to an agricultural effluent control management problem. IDFCCP was formulated through incorporating interval linear programming (ILP) into a double-sided fuzzy chance-constrained programming (DFCCP) framework, and could be used to deal with uncertainties expressed as not only possibility distributions associated with both left- and right-hand-side components of constraints but also discrete intervals in the objective function. The study results indicated that IDFCCP allowed violation of system constraints at specified confidence levels, where each confidence level consisted of two reliability scenarios. This could lead to model solutions with high system benefits under acceptable risk magnitudes. Furthermore, the introduction of ILP allowed uncertain information presented as discrete intervals to be communicated into the optimization process, such that a variety of decision alternatives can be generated by adjusting the decision-variable values within their intervals. The proposed model could help decision makers establish various production patterns with cost-effective water quality management schemes under complex uncertainties, and gain in-depth insights into the trade-offs between system economy and reliability. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Fuzzy chance-constrained programming interval linear programming Effluent control management Agricultural system Uncertainty

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Fuzzy two-stage non-point source pollution management model for agricultural systems-A case study for the Lake Tai Basin, China

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AGRICULTURAL WATER MANAGEMENT 2013年 121卷 27-41页

作者： Liu, M. Huang, G. H. Liao, R. F. Li, Y. P. Xie, Y. L. North China Elect Power Univ Resources & Environm Res Acad MOE Key Lab Reg Energy & Environm Syst Optimizat Beijing 102206 Peoples R China Univ Regina Fac Engn & Appl Sci Environm Syst Engn Program Regina SK S4S 0A2 Canada

Non-point source (NPS) pollution from agricultural lands has aroused widespread concerns throughout the world. In this study, an interval fuzzy two-stage stochastic non-point source pollution mitigation (IFTNS) model was developed for agricultural systems management under uncertainty through land retirement and nutrients discharge trading programs. The developed IFTNS model incorporated fuzzy possibilistic programming (FPP) and interval linear programming (ILP) within a general two-stage stochastic programming (TSP) framework. The IFTNS model could not only deal with uncertainties presented as probability density functions, fuzzy membership functions, and discrete interval numbers, but also provide an effective linkage between the pre-regulated agricultural systems management policies and the associated economic implications. Moreover, the IFTNS model could help to analyze various trading scenarios associated with different plausibility degree levels. The IFTNS model was applied to a case study with a nutrients discharge trading program within a subcatchment of the Lake Tai Basin in China. The results indicated that reasonable solutions under different plausibility degree levels were generated, which could be used for generating decision alternatives and thus help decision makers to identify desired agricultural NPS pollution mitigation policies. The results also indicated that land retirement and nutrients discharge trading programs could effectively achieve agricultural NPS pollution mitigation and maximize net system benefits. (c) 2013 Elsevier B.V. All rights reserved.

关键词： Agricultural non-point source pollution Land retirement Nutrients discharge trading Two-stage stochastic programming Fuzzy possibilistic programming interval linear programming

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An inexact double-sided chance-constrained model for air quality management in Nanshan District, Shengzhen, China

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ENGINEERING OPTIMIZATION 2014年第12期46卷 1694-1708页

作者： Shao, Liguo Xu, Ye Huang, Guohe China Ctr Informat Ind Dev Beijing Peoples R China North China Elect Power Univ MOE Key Lab Reg Energy & Environm Syst Optimizat Sinocanada Resources & Environm Res Acad Beijing Peoples R China

In this study, an inexact double-sided fuzzy-random-chance-constrained programming (IDSFRCCP) model was developed for supporting air quality management of the Nanshan District of Shenzhen, China, under uncertainty. IDSFRCCP is an integrated model incorporating interval linear programming and double-sided fuzzy-random-chance-constrained programming models. It can express uncertain information as both fuzzy random variables and discrete intervals. The proposed model was solved based on the stochastic and fuzzy chance-constrained programming techniques and an interactive two-step algorithm. The air quality management system of Nanshan District, including one pollutant, six emission sources, six treatment technologies and four receptor sites, was used to demonstrate the applicability of the proposed method. The results indicated that the IDSFRCCP was capable of helping decision makers to analyse trade-offs between system cost and risk of constraint violation. The mid-range solutions tending to lower bounds with moderate alpha(h) and q(i) values were recommended as decision alternatives owing to their robust characteristics.

关键词： chance-constrained programming interval linear programming air quality management uncertainty

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Efficient management of air quality considering fuzzy confidences with varied reliabilities

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ENGINEERING OPTIMIZATION 2012年第8期44卷 947-964页

作者： Xu, Y. Huang, G. H. Shao, L. G. Chen, C. N China Elect Power Univ Sino Canada Energy & Environm Res Acad Key Lab Reg Energy Syst Optimizat MOE Beijing 102206 Peoples R China Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Peking Univ Coll Environm Sci & Engn Beijing 100871 Peoples R China NE Normal Univ Coll Urban & Environm Sci Changchun 130024 Peoples R China

Regional air quality management systems are complicated by uncertainties due to their interactive, dynamic, and multi-objective features. In this study, an inexact double-sided fuzzy chance-constrained programming (IDFCCP) model was developed and applied to a hypothetical case of regional air quality management. The results indicated that the proposed IDFCCP improved upon the existing ILP and DFCCP approaches;the fuzzy confidences at different levels could be analysed with varied reliability scenarios, making it possible to handle fuzzy uncertainties originating from both sides of the model constraints;other uncertain parameters could be expressed in terms of discrete intervals. The trade-off between system economy and reliability could be analysed by decision makers according to their preferences. The study results demonstrated that the proposed method could help decision makers identify desired policies under various environmental, economic, system-feasibility and system-reliability constraints.

关键词： fuzzy chance-constrained programming interval linear programming air quality management uncertainty

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