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Inexact left-hand-side chance-constrained programming for Nonpoint-Source Water Quality Management

WATER AIR AND SOIL POLLUTION 2014年第3期225卷 1页

作者： Ji, Yao Huang, Guo H. Sun, Wei North China Elect Power Univ MOE Key Lab Reg Energy & Environm Syst Optimizat SC Resources & Environm Res Acad Beijing 102206 Peoples R China Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 0A2 Canada

An inexact left-hand-side chance-constrained programming (ILCCP) was proposed and applied to a nonpoint-source water quality management problem within an agricultural system. The ILCCP model can reflect uncertainties presented as interval parameters (manure mass balance, crop nutrient balances, energy and digestible protein requirements, pollutant losses, water quantity constraints, technical constraints, and so on) and left-hand-side random variables (nitrogen requirement of crop i) at the same time. A non-equivalent linearization form of ILCCP was deduced and proved intuitively, which can help handle the left-hand-side random parameters in the constraints. The decision schemes through ILCCP were analyzed under scenarios at different individual probabilities (pi, denotes the admissible probability of violating the constraint i). The performance of ILCCP was also compared with the corresponding interval linear programming model. A representative nonpoint-source water quality management case was employed to facilitate the analysis and the comparison. The optimization results indicated that the net system benefit in the water quality management case would decrease with increasing probability levels on the whole. This was because that the higher constraint satisfaction of probability would lead to stricter decision space. The optimal scheme shows an obvious downtrend in the application amount of manure as the violation probability levels decreasing from scenarios 1 to 3 (p(i)=0.1, 0.05 and 0.01). This demonstrates that the application amount of manure would be reduced effectively by adjusting strictness of the constraints. This study is the first application of the ILCCP model to water quality management, which indicates that the ILCCP is applicable to other environmental problems under uncertainties.

关键词： left-hand-side chance-constrained programming Water quality Uncertainty Agricultural system

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An interval multistage joint-probabilistic chance-constrained programming model with left-hand-side randomness for crop area planning under uncertainty

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JOURNAL OF CLEANER PRODUCTION 2017年第Nov.20期167卷 1276-1289页

作者： Zhang, Chenglong Li, Mo Guo, Ping China Agr Univ Ctr Agr Water Res China Tsinghuadong St 17 Beijing 100083 Peoples R China

The characteristics of the agricultural water management system is its great complexity and uncertainty as well as dynamic variations in the system components, which results in dynamic characteristics in optimizing the agricultural water allocation and crop area planning. In this study, an interval multistage joint-probabilistic left-hand-side chance-constrained programming (IMJLCP) model is developed for crop area planning in response to these issues. This method is derived from incorporating the techniques of multistage stochastic programming and joint-probabilistic left-hand-side chance-constrained programming within a general interval optimization framework. It can address uncertainties presented as both discrete intervals and probability distributions, and also reflect dynamic characteristics of the system conditions. Moreover, it can reflect randomness in the left-hand-side of the constraints and examine the reliability level of satisfying constraints at both joint and individual probabilities. The developed method is applied to a case study of dynamic agricultural water management and irrigated crop area planning in different growth stages in the middle reaches Of Heihe River Basin, taking ground water and surface water use into account. Six scenarios with different joint (i.e. p = 0.01, 0.05 and 0.1) and individual probabilities (i.e. same and increasing) of the irrigation quota are examined, and a multilayered scenario tree will be provided for a dynamic analysis in a planning horizon. The results indicate that different levels of constraints violation reflect the attitudes of managers to economic benefit and risk. Furthermore, it can help managers to identify desired decision alternatives in intra- and inter-seasonal water allocation among different crops in different subareas. This application makes it highly feasible to enhance the efficiency of irrigation water and ensure sustainable use of water resources, especially for the arid regions dominated by a

关键词： Crop area planning Agricultural irrigation Multistage stochastic programming left-hand-side chance-constrained programming Joint probabilistic programming Uncertainty

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Inexact joint-probabilistic chance-constrained programming with left-hand-side randomness: An application to solid waste management

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第1期228卷 217-225页

作者： Sun, Wei Huang, Guo H. Lv, Ying Li, Gongchen Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China

In practical waste management systems, amounts of waste transported and treated are not always equal on a daily basis. To distinguish between these two kinds of amounts and reflect their random relationships effectively, an inexact joint-probabilistic left-hand-side chance-constrained programming (IRCP) method was developed and applied to a municipal solid waste management problem under dual uncertainties. Dual uncertainties are defined as two kinds of uncertainties existing in the same programming model. Improving upon conventional right-hand-side chance-constrained programming, the ULCP can not only reflect uncertainties presented in terms of interval parameters (unit transportation/treatment costs, capacities of waste treatment facilities, waste generation rates, waste transportation/treatment amounts and so on) and left-hand-side random variables (the relationship between waste transportation and treatment amounts), but also examine the reliability of satisfying (or risk of violating) the entire system constraints. A non-equivalent but sufficient linearization form of ULCP for solving this type of problem was proposed and proved in a straightforward manner. The performance of ULCP was analyzed under scenarios at joint and individual probabilities and compared with the corresponding internal-parameter programming model. The results indicated that the net system costs would both decrease with increasing joint probability levels and decrease slightly at different individual probabilities with the same joint probabilities. The two types of dual uncertainties were discussed as well. (C) 2013 Elsevier B.V. All rights reserved.

关键词： (D) OR in natural resources left-hand-side chance-constrained programming Waste management Joint probabilistic programming Dual uncertainty

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