A refined risk explicit interval linear programming approach for optimal watershed load reduction with objective-constraint uncertainty tradeoff analysis

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

References

[1] Conley D J. Biogeochemical nutrient cycles and nutrient management strategies. Hydrobiologia, 2000, 410: 87−96

[2] National Research Council. Assessing the TMDL Approach to Water Quality Management. Washington, DC: National Academy Press, 2001

[3] Diaz R J, Rosenberg R. Spreading dead zones and consequences for marine ecosystems. Science, 2008, 321(5891): 926−929

[4] Liu Y, Guo H C, Yu Y J, Dai Y L, Zhou F. Ecological-economic modeling as a tool for lake-watershed management: a case study of Lake Qionghai Watershed, China. Limnologica-Ecology and Management of Inland Waters, 2008, 38(2): 89−104

[5] Conley D J, Paerl H W, Howarth R W, Boesch D F, Seitzinger S P, Havens K E, Lancelot C, Likens G E. Ecology. Controlling eutrophication: nitrogen and phosphorus. Science, 2009, 323(5917): 1014−1015

[6] Voinov A, Gaddis E B. Lessons for successful participatory watershed modeling: a perspective from modeling practitioners. Ecological Modelling, 2008, 216(2): 197−207

[7] Liu Y, Zou R, Riverson J, Yang P J, Guo H C. Guided adaptive optimal decision making approach for uncertainty based watershed scale load reduction. Water Research, 2011, 45(16): 4885−4895

[8] Ayyub B MUncertainty Modeling and Analysis in Civil Engineering. Boca Raton, FL: CRC Press, 1998

[9] Oberkampf W L, DeLand S M, Rutherford B M, Diegert K V, Alvin K F. Error and uncertainty in modeling and simulation. Reliability Engineering & System Safety, 2002, 75(3): 333−357

[10] Baresel C, Destouni G. Uncertainty-accounting environmental policy and management of water systems. Environmental science & technology, 2007, 41(10): 3653−3659

[11] Pintér J. Stochastic modelling and optimization for environmental management. Annals of Operations Research, 1991, 31(1): 527−544

[12] Kerachian R, Karamouz M. A stochastic conflict resolution model for water quality management in reservoir-river systems. Advances in Water Resources, 2007, 30(4): 866−882

[13] Ghosh S, Suresh H R, Mujumdar P P. Fuzzy waste load allocation model: application to a case study. Journal of Intelligent Systems, 2009, 17(1−3): 283−296

[14] Nikoo M R, Kerachian R, Karimi A. A nonlinear interval model for water and waste load allocation in river basins. Water resources management, 2012, 26(10): 2911−2926

[15] Luo B, You J. A watershed-simulation and hybrid optimization modeling approach for water-quality trading in soil erosion control. Advances in water resources, 2007, 30(9): 1902−1913

[16] Rommelfanger H. Fuzzy linear programming and applications. Journal of Operational Research, 1996, 92(3): 512−527

[17] Chang N B, Chen H W, Shaw D G, Yang C H. Water pollution control in a river basin by interactive fuzzy interval multi-objective programming. Journal of Environmental Engineering, 1997, 123(12): 1208−1216

[18] Zou R, Liu Y, Liu L, Guo H C. REILP approach for uncertainty-based decision making in civil engineering. Journal of Computing in Civil Engineering, 2009, 24(4): 357−364

[19] Rommelfanger H, Hanuscheck R, Wolf J. Linear programming with fuzzy objectives. Fuzzy Sets and Systems, 1989, 29(1): 31−48

[20] Huang G H, Cohen S J, Yin Y Y, Bass B. Incorporation of inexact dynamic optimization with fuzzy relation analysis for integrated climate change impact study. Journal of Environmental Management, 1996, 48(1): 45−68

[21] Li Y P, Huang G H. An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina. Journal of Environmental Management, 2006, 81(3): 188−209

[22] Wu S M, Huang G H, Guo H C. An interactive inexact-fuzzy approach for multiobjective planning of water resource systems. Water Science and Technology, 1997, 36(5): 235−242

[23] Qin X S, Huang G H, Zeng G M, Chakma A, Huang Y F. An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty. European Journal of Operational Research, 2007, 180(3): 1331−1357

[24] Ozdemir M S, Saaty T L. The unknown in decision making: what to do about it. European Journal of Operational Research, 2006, 174(1): 349−359

[25] Fiedler M, Nedoma J, Ramik J, Rohn J, Zimmermann KLinear Optimization Problems with Inexact Data. New York: Springer, 2006

[26] Liu Y, Zou R, Guo H C. A risk explicit interval linear programming model for uncertainty-based nutrient-reduction optimization for the Lake Qionghai. Journal of Water Resources Planning and Management, 2011, 137(1): 83−91

[27] Wen C G, Lee C S. A neural network approach to multiobjective optimization for water quality management in a river basin. Water Resources Research, 1998, 34(3): 427−436

[28] Rodriguez H G, Popp J, Maringanti C, Chaube I. Selection and placement of best management practices used to reduce water quality degradation in Lincoln Lake watershed. Water Resources Research, 2011, 47(1): 1−13

[29] Peña-Haro S, Pulido-Velazquez M, Llopis-Albert C. Stochastic hydro-economic modeling for optimal management of agricultural groundwater nitrate pollution under hydraulic conductivity uncertainty. Environmental Modelling & Software, 2011, 26(8): 999−1008

[30] Hansen E R, Walster G WGlobal Optimization Using Interval Analysis. 2nd edition. New York: CRC Press, 2004

[31] Tong S C. Interval number, fuzzy number linear programming. Fuzzy Sets and Systems, 1994, 66(3): 301−306 doi:10.1016/0165-0114(94)90097-3

[32] Liu Y, Guo H C, Zhou F, Qin X S, Huang K, Yu Y J. Inexact chance-constrained linear programming model for optimal water pollution management at the watershed scale. Journal of Water Resources Planning and Management, 2008, 134(4): 347−356

[33] Liu Y, Guo H C, Zhang Z X, Wang L J, Dai Y L, Fan Y Y. An optimization method based on scenario analysis for watershed management under uncertainty. Environmental Management, 2007, 39(5): 678−690

[34] Kramer D B, Polasky S, Starfield A, Palik B, Westphal L, Snyder S, Jakes P, Hudson R, Gustafson E. A comparison of alternative strategies for cost-effective water quality management in lakes. Environmental Management, 2006, 38(3): 411−425

[35] Young R A. Uncertainty and the Environment: Implications for Decision Making and Environmental Policy. Cheltenham: Edward Elgar Pub, 2001

Acknowledgements

This paper was supported by the National Natural Science Foundation of China (Grant No. 41222002), Research Fund for the Doctoral Program of Higher Education of China (20100001120020) and “China National Water Pollution Control Program” (2013ZX07102-006). Special thanks to Dr. Daniel Obenour in University of Michigan.

Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s11783-014-0683-8 and is accessible for authorized users.

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg