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Frontiers of Environmental Science & Engineering

ISSN 2095-2201

ISSN 2095-221X(Online)

CN 10-1013/X

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Front. Environ. Sci. Eng.    2016, Vol. 10 Issue (1) : 129-140    https://doi.org/10.1007/s11783-014-0683-8
RESEARCH ARTICLE
A refined risk explicit interval linear programming approach for optimal watershed load reduction with objective-constraint uncertainty tradeoff analysis
Pingjian YANG1,2,Feifei DONG1,Yong LIU1,3,Rui ZOU4,*(),Xing CHEN1,Huaicheng GUO1,*
1. College of Environmental Science and Engineering, Peking University, the Key Laboratory of Water and Sediment Sciences, Ministry of Education, Beijing 100871, China
2. School of Natural Resources and Environment, University of Michigan, Ann Arbor, MI 48109, USA
3. Yunnan International Center for Pleantu Lakes, Kunming 650034, China
4. Tetra Tech, Inc. Fairfax, VA 22030, USA
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Abstract

To enhance the effectiveness of watershed load reduction decision making, the Risk Explicit Interval Linear Programming (REILP) approach was developed in previous studies to address decision risks and system returns. However, REILP lacks the capability to analyze the tradeoff between risks in the objective function and constraints. Therefore, a refined REILP model is proposed in this study to further enhance the decision support capability of the REILP approach for optimal watershed load reduction. By introducing a tradeoff factor (α) into the total risk function, the refined REILP can lead to different compromises between risks associated with the objective functions and the constraints. The proposed model was illustrated using a case study that deals with uncertainty-based optimal load reduction decision making for Lake Qionghai Watershed, China. A risk tradeoff curve with different values of α was presented to decision makers as a more flexible platform to support decision formulation. The results of the standard and refined REILP model were compared under 11 aspiration levels. The results demonstrate that, by applying the refined REILP, it is possible to obtain solutions that preserve the same constraint risk as that in the standard REILP but with lower objective risk, which can provide more effective guidance for decision makers.
Keywords refined risk explicit interval linear programming      decision making      objective-constraint uncertainty tradeoff      aspiration level      Lake Qionghai Watershed     
Corresponding Author(s): Rui ZOU,Huaicheng GUO   
Online First Date: 25 March 2014    Issue Date: 03 December 2015
 Cite this article:   
Pingjian YANG,Feifei DONG,Yong LIU, et al. A refined risk explicit interval linear programming approach for optimal watershed load reduction with objective-constraint uncertainty tradeoff analysis[J]. Front. Environ. Sci. Eng., 2016, 10(1): 129-140.
 URL:  
https://academic.hep.com.cn/fese/EN/10.1007/s11783-014-0683-8
https://academic.hep.com.cn/fese/EN/Y2016/V10/I1/129
Fig.1  Study area (modified from Liu et al. [32])
Fig.2  Objective-Constraint risks curve
strategies S7 R7,1 R7,2 R7,3
standard percentage α= 0.01 percentage standard percentage α= 0.01 percentage
j = 1 24.75 13.18 24.75 13.19 24.75 13.19 24.75 13.20
j = 2 7.39 3.94 7.39 3.94 7.39 3.94 7.39 3.94
j = 3 5.42 2.88 5.42 2.88 5.42 2.88 5.42 2.89
j = 4 5.40 2.88 5.40 2.88 5.40 2.88 5.40 2.88
j = 5 42.63 22.70 42.63 22.71 42.63 22.71 42.69 22.76
j = 6 69.01 36.75 69.00 36.75 69.12 36.82 71.47 38.11
j = 7 3.43 1.82 3.43 1.83 3.43 1.83 3.43 1.83
j = 8 27.75 14.78 27.75 14.78 27.62 14.71 25.01 13.34
j = 9 0.65 0.35 0.63 0.34 0.63 0.34 0.63 0.34
j = 10 1.35 0.72 1.35 0.72 1.35 0.72 1.35 0.72
total 187.77 100.00 187.74 100.00 187.73 100.00 187.54 100.00
Tab.1  Refined REILP and standard REILP among different strategies
Fig.3  Load reduction (t·a−1) for different strategies of the refined REILP (R7,2) and standard REILP (S7) under aspiration levels= 0.7 and risk tradeoff= 0.1
standard (S7) percentage α = 0.01(R7,1) percentage α = 0.1(R7,2) percentage α = 1(R7,3) percentage
sub-watershed S7 R7,1 R7,2 R7,2R7,3
standard percentage α = 0.01 percentage standard percentage α = 0.01 percentage
i = 1 6.67 3.55 6.67 3.55 6.65 3.54 6.28 3.35
i = 2 0.58 0.31 0.58 0.31 0.57 0.31 0.52 0.28
i = 3 11.96 6.37 78.59 41.86 11.93 6.36 73.61 39.25
i = 4 5.41 2.88 5.40 2.88 5.39 2.87 5.17 2.76
i = 5 70.40 37.49 6.50 3.46 6.83 3.64 6.23 3.32
i = 6 6.37 3.39 6.32 3.37 6.31 3.36 6.06 3.23
i = 7 1.00 0.53 0.96 0.51 0.95 0.51 0.86 0.46
i = 8 12.20 6.50 12.20 6.50 12.20 6.50 12.20 6.51
i = 9 6.69 3.56 5.71 3.04 5.70 3.04 5.61 2.99
i = 10 4.04 2.15 4.69 2.50 3.78 2.01 3.59 1.92
i = 11 16.80 8.95 16.87 8.98 75.42 40.18 16.36 8.72
i = 12 0.74 0.39 0.03 0.02 1.58 0.84 1.46 0.78
i = 13 1.32 0.70 0.83 0.44 1.83 0.98 1.74 0.93
i = 14 1.51 0.81 1.50 0.80 2.57 1.37 2.17 1.16
i = 15 1.26 0.67 1.50 0.80 1.91 1.02 1.17 0.63
i = 16 4.15 2.21 5.03 2.68 5.06 2.69 4.94 2.63
i = 17 1.43 0.76 0.95 0.51 0.96 0.51 1.97 1.05
i = 18 1.11 0.59 0.06 0.03 3.07 1.64 2.67 1.42
i = 19 1.12 0.60 0.35 0.19 2.00 1.07 1.90 1.01
i = 20 33.01 17.58 33.01 17.58 33.01 17.58 33.01 17.60
total 187.77 100.00 187.74 100.00 187.73 100.00 187.54 100.00
Tab.2  Refined REILP and standard REILP among different sub-watersheds
Fig.4  Load reduction (t·a−1) for different sub-watersheds of refined REILP (R7,2) and standard REILP (S7) under aspiration levels= 0.7 and risk tradeoff= 0.1
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