Two-stage planning for sustainable water-quality management under uncertainty.

In water-quality management problems, uncertainties may exist in a number of impact factors and pollution-related processes (e.g., the volume and strength of industrial wastewater and their variations can be presented as random events through identifying a statistical distribution for each source); moreover, nonlinear relationships may exist among many system components (e.g., cost parameters may be functions of wastewater-discharge levels). In this study, an inexact two-stage stochastic quadratic programming (ITQP) method is developed for water-quality management under uncertainty. It is a hybrid of inexact quadratic programming (IQP) and two-stage stochastic programming (TSP) methods. The developed ITQP can handle not only uncertainties expressed as probability distributions and interval values but also nonlinearities in the objective function. It can be used for analyzing various scenarios that are associated with different levels of economic penalties or opportunity losses caused by improper policies. The ITQP is applied to a case of water-quality management to deal with uncertainties presented in terms of probabilities and intervals and to reflect dynamic interactions between pollutant loading and water quality. Interactive and derivative algorithms are employed for solving the ITQP model. The solutions are presented as combinations of deterministic, interval and distributional information, and can thus facilitate communications for different forms of uncertainties. They are helpful for managers in not only making decisions regarding wastewater discharge but also gaining insight into the tradeoff between the system benefit and the environmental requirement.

[1]  Subhankar Karmakar,et al.  An inexact optimization approach for river water-quality management. , 2006, Journal of environmental management.

[2]  Jonathan Lawry,et al.  River Flow Modelling Using Fuzzy Decision Trees , 2002 .

[3]  Gordon H. Huang,et al.  A derivative algorithm for inexact quadratic program - application to environmental decision-making under uncertainty , 2001, Eur. J. Oper. Res..

[4]  Ni-Bin Chang,et al.  Water pollution control in the river basin by fuzzy genetic algorithm-based multiobjective programming modeling , 1998 .

[5]  Jitka Dupacová,et al.  Applications of stochastic programming: Achievements and questions , 2002, Eur. J. Oper. Res..

[6]  Subhankar Karmakar,et al.  A two-phase grey fuzzy optimization approach for water quality management of a river system , 2007 .

[7]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[8]  G H Huang,et al.  Inexact multistage stochastic integer programming for water resources management under uncertainty. , 2008, Journal of environmental management.

[9]  A. Ruszczynski,et al.  Accelerating the regularized decomposition method for two stage stochastic linear problems , 1997 .

[10]  R. Słowiński A multicriteria fuzzy linear programming method for water supply system development planning , 1986 .

[11]  Guohe Huang,et al.  AN INEXACT TWO-STAGE STOCHASTIC PROGRAMMING MODEL FOR WATER RESOURCES MANAGEMENT UNDER UNCERTAINTY , 2000 .

[12]  R. Thomann,et al.  Principles of surface water quality modeling and control , 1987 .

[13]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[14]  Warren Viessman,et al.  Water supply and pollution control , 1985 .

[15]  P. P. Mujumdar,et al.  Grey fuzzy optimization model for water quality management of a river system , 2006 .

[16]  Guillermo J. Vicens,et al.  A Bayesian framework for the use of regional information in hydrology , 1975 .

[17]  N B Chang,et al.  Identification of river water quality using the fuzzy synthetic evaluation approach. , 2001, Journal of environmental management.

[18]  Leon S. Lasdon,et al.  A scenario-based stochastic programming model for water supplies from the highland lakes , 2000 .

[19]  W. R. Buckland,et al.  Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. , 1952 .

[20]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[21]  G. H. Huang,et al.  A hybrid inexact-stochastic water management model , 1998, Eur. J. Oper. Res..

[22]  Jr W. Wesley Eckenfelder Industrial Water Pollution Control , 1967 .

[23]  J. Eheart,et al.  Aquifer remediation design under uncertainty using a new chance constrained programming technique , 1993 .

[24]  Chih-Sheng Lee,et al.  Interactive fuzzy optimization for an economic and environmental balance in a river system. , 2005, Water research.

[25]  Gareth Pender,et al.  Field Measurements and Flow Modeling of Overbank Flows in River Severn, U.K. , 2003 .

[26]  Douglas A. Haith Environmental systems optimization , 1982 .

[27]  N. Grigg Water Resources Planning , 1985 .

[28]  Keith W. Hipel,et al.  Interior-Point Method for Reservoir Operation with Stochastic Inflows , 2001 .

[29]  S. M. Wu,et al.  An interactive inexact-fuzzy approach for multiobjective planning of water resource systems , 1997 .

[30]  Charles ReVelle,et al.  A siting model for regional wastewater treatment systems: The chain configuration case , 1988 .

[31]  Y. P. Li,et al.  Mixed interval–fuzzy two-stage integer programming and its application to flood-diversion planning , 2007 .

[32]  Gordon H. Huang,et al.  An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty , 2006 .

[33]  Guohe Huang,et al.  GREY QUADRATIC PROGRAMMING AND ITS APPLICATION TO MUNICIPAL SOLID WASTE MANAGEMENT PLANNING UNDER UNCERTAINTY , 1995 .

[34]  G H Huang,et al.  An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina. , 2006, Journal of environmental management.

[35]  J. Stedinger,et al.  Water resource systems planning and analysis , 1981 .

[36]  Gordon H. Huang,et al.  IPWM: AN INTERVAL PARAMETER WATER QUALITY MANAGEMENT MODEL , 1996 .

[37]  Y. P. Li,et al.  Fuzzy two-stage quadratic programming for planning solid waste management under uncertainty , 2007, Int. J. Syst. Sci..

[38]  Shabbir Ahmed,et al.  A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty , 2003, J. Glob. Optim..