Simulation-Based Inexact Two-Stage Chance-Constraint Quadratic Programming for Sustainable Water Quality Management under Dual Uncertainties
Publication: Journal of Water Resources Planning and Management
Volume 140, Issue 3
Abstract
Water quality planning is complicated itself but further challenged by the existence of uncertainties and nonlinearities in terms of model formulation and solution. In this study, a simulation-based inexact two-stage chance-constraint quadratic programming (SITCQP) approach was developed for water quality management. The SITCQP model was a hybrid of two-stage stochastic programming (TSP), chance-constraint programming (CCP), inexact quadratic programming (IQP), and multisegment stream water quality simulation. A water quality simulation model was provided for reflecting the relationship between the pollution-control actions before wastewater discharge and the environmental responses after the discharge. Interval quadratic polynomials were employed to reflect the uncertainties and nonlinearities associated with the costs for wastewater treatment. Uncertainties derived from water quality standards were characterized as random variables with normal distributions. The proposed approach was applied to a hypothetical case in water quality management. The modeling solutions were presented as combinations of deterministic, interval and distributional information, which could facilitate predictions for different forms of uncertainties. The results were valuable for helping decision makers generate alternatives between wastewater treatment and stream water quality management.
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Acknowledgments
The research was supported by the National Natural Science Foundation of China (No. 51179070), Natural Science and Engineering Research Council of Canada, and United Nations Development Programme. The authors deeply appreciate the editors and the anonymous reviewers for their insightful comments and suggestions.
References
Alp, E., and Melching, C. S. (2009). “Evaluation of the duration of storm effects on in-stream water quality.” J. Water Resour. Plann. Manage., 107–116.
Babaeyan-Koopaei, K., Ervine, D. A., and Pender, G. (2003). “Field measurements and flow modeling of overbank flows in River Severn, UK.” J. Environ. Inform., 1(1), 28–36.
Chang, N. B., Chen, H. W., and Ning, S. K. (2001). “Identification of river water quality using the fuzzy synthetic evaluation approach.” J. Environ. Manage., 63(3), 293–305.
Charnes, A., and Cooper, W. W. (1983). “Response to decision problems under risk and chance constrained programming: Dilemmas in the transitions.” Manage. Sci., 29(6), 750–763.
Charnes, A., Cooper, W. W., and Kirby, P. (1972). “Chance constrained programming: An extension of statistical method.” Optimizing methods in statistics, Academic Press, New York, 391–402.
Chen, H. W., and Chang, N. B. (1998). “Water pollution control in the river basin by genetic algorithm-based fuzzy multi-objective programming modeling.” Water Sci. Technol., 37(8), 55–63.
Chen, M. J., and Huang, G. H. (2001). “A derivative algorithm for inexact quadratic program application to environmental decision-making under uncertainty.” Eur. J. Oper. Res., 128(3), 570–586.
Cox, B. A. (2003). “A review of currently available in-stream water-quality models and their applicability for simulating dissolved oxygen in lowland rivers.” Sci. Total Environ., 314–316, 335–377.
Cunha, M. C., Pinheiro, L., Zeferino, J., Antunes, A., and Afonso, P. (2009). “Optimization model for integrated regional wastewater systems planning.” J. Water Resour. Plan. Manage., 23–33.
Eckenfelder, W. W., Jr. (2000). Industrial water pollution control, 3rd Ed., McGraw-Hill, Columbus, OH.
Franceschini, S., and Tsai, C. W. (2010). “Assessment of uncertainty sources in water quality modeling in the Niagara River.” Adv. Water Resour., 33(4), 493–503.
Grigg, N. S. (1985). Water resources planning, McGraw-Hill.
Haith, A. D. (1982). Environmental systems optimization, John Wiley and Sons, New York.
Hu, M., Huang, G. H., Sun, W., and Li, Y. P. (2012). “Inexact quadratic joint-probabilistic programming for water quality management under uncertainty in the Xiangxi River, China.” Stochastic Environ. Res. Risk Assess., 27(5), 1115–1132.
Huang, G. H. (1998). “A hybrid inexact-stochastic water management model.” Eur. J. Oper. Res., 107(1), 137–158.
Huang, G. H., Baetz, B. W., and Patry, G. G. (1995). “Grey quadratic programming and its application to municipal waste management planning under uncertainty.” Eng. Optimiz., 23(3), 210–223.
Huang, G. H., and Chang, N. B. (2003). “The perspectives of environmental informatics and systems analysis.” J. Environ. Inform., 1(1), 1–6.
Huang, G. H., and Loucks, D. P. (2000). “An inexact two-stage stochastic programming model for water resources management under uncertainty.” Civ. Eng. Environ. Syst., 17(2), 95–118.
Jan, C., Steven, B., and Veronique, V. (2011). “Coupling a hydrological water quality model and an economic optimization model to set up a cost-effective emission reduction scenario for nitrogen.” Environ. Model. Softw., 26(1), 44–51.
Karmakar, S., and Mujumdar, P. P. (2007). “A two-phase grey fuzzy optimization approach for water quality management of a river system.” Adv. Water Resour., 30(5), 1218–1235.
Kerachinan, R., and Karamouz, M. (2007). “A stochastic conflict resolution model for water quality management in reservoir-river systems.” Adv. Water Resour., 30(4), 866–882.
Kotti, M. E., Vlessidis, A. G., Thanasoulias, N. C., and Evmiridis, N. P. (2005). “Assessment of river water quality in Northwestern Greece.” Water Resour. Manage., 19(1), 77–94.
Lee, C. S., and Chang, S. P. (2005). “Interactive fuzzy optimization for an economic and environmental balance in a river system.” Water Res., 39(1), 221–231.
Li, P., and Chen, B. (2011). “FSILP: Fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.” J. Environ. Manage., 92(4), 1198–1209.
Li, P., Chen, B., Zhang, B. Y., Jing, L., and Zheng, J. S. (2012). “A multiple-stage simulation-based mixed integer nonlinear programming approach for supporting offshore oil spill recovery with weathering process.” J. Ocean Tech., 7(4), 87–105.
Li, P., Wu, H. J., and Chen, B. (2013). “RSW-MCFP: A resource-oriented solid waste management system for a mixed rural-urban area through monte carlo simulation-based fuzzy programming.” Math. Prob. Eng., 2013(2013), 15.
Li, Y. P., and Huang, G. H. (2007). “Fuzzy two-stage quadratic programming for planning solid waste management under uncertainty.” Int. J. Syst. Sci., 38(3), 219–233.
Li, Y. P., and Huang, G. H. (2009). “Two-stage planning for sustainable water-quality management under uncertainty.” J. Environ. Manage., 90(8), 2402–2413.
Li, Y. P., Huang, G. H., and Nie, S. L. (2007). “Mixed interval-fuzzy two-stage integer programming and its application to flood-diversion planning.” Eng. Optimiz., 39(2), 163–183.
Liu, L., Huang, G. H., Liu, Y., and Fuller, G. A. (2003). “A fuzzy-stochastic robust programming model for regional air quality management under uncertainty.” Eng. Optimiz., 35(2), 177–199.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1981). Water resource systems planning and analysis, Prentice-Hall, Englewood Cliffs, NJ.
Luo, B., Li, J. B., Huang, G. H., and Li, H. L. (2006). “A simulation-based interval two-stage stochastic model for agricultural nonpoint source pollution control through land retirement.” Sci. Total Environ., 361(1–3), 38–56.
Maqsood, I., Huang, G. H., and Yeomans, J. S. (2005). “An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty.” Eur. J. Oper. Res., 167(1), 208–225.
Morgan, D. R., Eheart, J. W., and Valocchi, A. J. (1993). “Aquifer remediation design under uncertainty using a new chance constrained programming technique.” Water Resour. Res., 29(3), 551–568.
Mujumdar, P. P., and Saxena, P. (2004). “A stochastic dynamic programming model for stream water quality management.” Sadhana, 29(5), 477–497.
Murty, Y. S. R., Bhallamudi, S. M., and Srinivasan, K. (2006). “Non-uniform flow effect on optimal waste loadallocation in rivers.” Water Resour. Manage., 20(4), 509–530.
O’Connor, D. J., and Dobbins, W. E. (1958). “Mechanisms of reaeration in natural streams.” Trans. ASCE, 123, 641–684.
Perlman, L., and Ostfeld, A. (2008). “Water distribution system aggregation for water quality analysis.” J. Water Resour. Plann. Manage., 303–309.
Qin, X. S., and Huang, G. H. (2009). “An inexact chance-constrained quadratic programming model for stream water quality management.” Water Resour. Manage., 23(4), 661–695.
Qin, X. S., Huang, G. H., Chen, B., and Zhang, B. Y. (2009). “An interval-parameter waste-load-allocation model for river waster quality management under uncertainty.” Environ. Manage., 43(6), 999–1012.
Rauch, W., et al. (1998). “River water quality modelling—I. State of the art.” Proc., IAWQ Biennial Int. Conf., Water Sci. Technol., 38(11), 237–244.
Ray, P. A., Kirshen, P. H., and Vogel, R. M. (2010). “Integrated optimization of a dual quality water and wastewater system.” J. Water Resour. Plann. Manage., 37–47.
Reichold, L., Zechman, E. M., Brill, E. D., and Holmes, H. (2010). “Simulation-optimization framework to support sustainable watershed development by mimicking the predevelopment flow regime.” J. Water Resour. Plann. Manage., 366–375.
Revelli, R., and Ridolfi, L. (2004). “Stochastic dynamics of BOD in a stream with random inputs.” Adv. Water Resour., 27(9), 943–952.
Ruszczynski, A., and Swietanowski, A. (1997). “Accelerating the regularized decomposition method for two-stage stochastic linear problems.” Eur. J. Oper. Res., 101(2), 328–342.
Sechi, G. M., and Sulis, A. (2009). “Water system management through a mixed optimization-simulation approach.” J. Water Resour. Plann. Manage., 160–170.
Seifi, A., and Hipel, K. W. (2001). “Interior-point method for reservoir operation with stochastic inflows.” J. Water Resour. Plann. Manage., 48–57.
State Environmental Protection Administration (SEPA). (1996). “Industrial wastewater discharge standard.”, Beijing.
State Environmental Protection Administration (SEPA). (2002). “Environmental quality standard for surface water.”, Beijing.
Thomann, R. V., and Mueller, J. A. (1987). Principles of surface water quality modeling and control, Harper and Row, New York.
Thuesen, H. G., Fabrycky, W. J., and Thuesen, G. J. (1977). Engineering economy, Prentice-Hall, Englewood Cliffs, NJ.
van Gils Ir, J. A. G, and Argiropoulos, D. (1991). “Axios River basin water quality management.” Water Resour. Manage., 5(3–4), 271–280.
Vicens, G. J., Rodriguez, I. I., and Schaake, J. C., Jr. (1975). “A Bayesian framework for the use of regional information in hydrology.” Water Resour. Res., 11(3), 405–414.
Wen, C. G., and Lee, C. S. (1998). “A neural network approach to multiobjective optimization for water quality management in a river basin.” Water Resour. Res., 34(3), 427–436.
Wu, S. M., Huang, G. H., and Guo, H. C. (1997). “An interactive inexact-fuzzy approach for multiobjective planning of water resources systems.” Water Sci. Technol., 36(5), 235–242.
Xie, Y. L., Li, Y. P., Huang, G. H., Li, Y. F., and Chen, L. R. (2011). “An inexact chance-constrained programming model for water quality management in Binhai New Area of Tianjin, China.” Sci. Total Environ., 409(10), 1757–1773.
Xu, Y., and Qin, X. S. (2010). “Agricultural effluent control under uncertainty: an inexact double-sided fuzzy chance-constrained model.” Adv. Water Resour., 33(9), 997–1014.
Yang, N., and Wen, F. (2005). “A chance constrained programming approach to transmission system expansion planning.” Electr. Power Syst. Res., 75(2–3), 171–177.
Zhang, X. D., Huang, G. H., and Nie, X. H. (2009). “Optimal decision schemes for agricultural water quality management planning with imprecise objective.” Ag. Water Manage., 96(12), 1723–1731.
Zhang, X. D., Huang, G. H., Nie, X. H., and Lin, Q. G. (2011). “Model-based decision support system for water quality management under hybrid uncertainty.” Expert Syst. Appl., 38(3), 2809–2816.
Zou, R., and Lung, W. S. (2004). “Robust water quality model calibration using an alternating fitness genetic algorithm.” J. Water Resour. Plann. Manage., 471–479.
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© 2014 American Society of Civil Engineers.
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Received: Jun 4, 2012
Accepted: Oct 30, 2012
Published online: Nov 3, 2012
Discussion open until: Apr 3, 2013
Published in print: Mar 1, 2014
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