Development of an inexact two-stage stochastic model with downside risk control for water quality management and decision analysis under uncertainty

Water quality management along rivers involves making water-allocation plans, establishing water quality goals, and controlling pollutant discharges, which is complicated itself but further challenged by existence of uncertainties. In this study, an inexact two-stage stochastic downside risk-aversion programming (ITSDP) model is developed for supporting regional water resources allocation and water quality management problems under uncertainties. The ITSDP method is a hybrid of interval-parameter programming, two-stage stochastic programming, and downside risk measure to tackle uncertainties described in terms of interval values and probability distributions. A water quality simulation model was provided for reflecting the relationship between the water resources allocation, wastewater discharge, and environmental responses. The proposed approach was applied to a hypothetical case for a shared stream water quality management with one municipal, three industrial and two agricultural sectors. A number of scenarios corresponding to different river inflows and risk levels were examined. The results demonstrated that the model could effectively communicate the interval-format and random uncertainties, and risk-aversion into optimization process, and generate a trade-off between the system economy and stability. They could be helpful for seeking cost-effective management strategies under uncertainties, and gaining an in-depth insight into the water quality management system characteristics, and make cost-effective decisions.

[1]  Miguel J. Bagajewicz,et al.  New measures and procedures to manage financial risk with applications to the planning of gas commercialization in Asia , 2004, Comput. Chem. Eng..

[2]  Y. F. Li,et al.  An inexact two-stage stochastic programming model for water resources management in Nansihu Lake Basin, China. , 2013, Journal of environmental management.

[3]  Guo H. Huang,et al.  A two-stage programming approach for water resources management under randomness and fuzziness , 2010, Environ. Model. Softw..

[4]  William Ocampo-Duque,et al.  Water quality analysis in rivers with non-parametric probability distributions and fuzzy inference systems: application to the Cauca River, Colombia. , 2013, Environment international.

[5]  Michael Matthies,et al.  System analysis of water quality management for the Elbe river basin , 2006, Environ. Model. Softw..

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

[7]  M. Zarghami,et al.  Stochastic-fuzzy multi criteria decision making for robust water resources management , 2009 .

[8]  Bing Chen,et al.  ITOM: an interval-parameter two-stage optimization model for stochastic planning of water resources systems , 2005 .

[9]  F. Sortino,et al.  Performance Measurement in a Downside Risk Framework , 1994 .

[10]  Guohe Huang,et al.  An inexact programming approach for supporting ecologically sustainable water supply with the consideration of uncertain water demand by ecosystems , 2011 .

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

[12]  Robert L. Smith,et al.  Capacity Expansion Under Stochastic Demands , 1992, Oper. Res..

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

[14]  Fereidoun Mobasheri,et al.  A two‐stage optimization model for design of a multipurpose reservoir , 1970 .

[15]  Endre Boros,et al.  A two-stage approach for large-scale sewer systems design with application to the Lake Balaton resort area , 1986 .

[16]  Eswaran Subrahmanian,et al.  Design and planning under uncertainty: issues on problem formulation and solution , 2003, Comput. Chem. Eng..

[17]  Guohe Huang,et al.  The Perspectives of Environmental Informatics and Systems Analysis , 2003 .

[18]  Chunhui Li,et al.  An inexact two-stage water management model for planning agricultural irrigation under uncertainty , 2010 .

[19]  John M. Mulvey,et al.  Formulating Two-Stage Stochastic Programs for Interior Point Methods , 1991, Oper. Res..

[20]  Luis S. Pereira,et al.  Multi-scale modeling for water resources planning and management in rural basins , 2005 .

[21]  Gordon H. Huang,et al.  Two-stage planning for sustainable water-quality management under uncertainty. , 2009, Journal of environmental management.

[22]  B. N. Lohani,et al.  Stochastic programming model for water quality management in a river , 2016 .

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

[24]  Mohammad Reza Nikoo,et al.  A Nonlinear Interval Model for Water and Waste Load Allocation in River Basins , 2012, Water Resources Management.

[25]  Pu Li,et al.  Simulation-Based Inexact Two-Stage Chance-Constraint Quadratic Programming for Sustainable Water Quality Management under Dual Uncertainties , 2014 .

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

[27]  K. Sasikumar,et al.  Application of fuzzy probability in water quality management of a river system , 2000, Int. J. Syst. Sci..

[28]  Gordon H. Huang,et al.  Inexact two-stage stochastic credibility constrained programming for water quality management , 2013 .

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

[30]  G H Huang,et al.  An inexact chance-constrained programming model for water quality management in Binhai New Area of Tianjin, China. , 2011, The Science of the total environment.

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

[32]  Guohe Huang,et al.  Inexact two-stage stochastic robust optimization model for water resources management under uncertainty. , 2009 .

[33]  Bing Chen,et al.  An Interval-Parameter Waste-Load-Allocation Model for River Water Quality Management Under Uncertainty , 2009, Environmental management.

[34]  Reza Kerachian,et al.  A stochastic conflict resolution model for trading pollutant discharge permits in river systems , 2009, Environmental monitoring and assessment.

[35]  Robert Finger Expanding risk consideration in integrated models - The role of downside risk aversion in irrigation decisions , 2013, Environ. Model. Softw..

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

[37]  Z. Yu,et al.  Spatial energy market risk analysis. I. An introduction to downside risk measures , 2002, 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309).

[38]  Guohe Huang,et al.  Managing water resources system in a mixed inexact environment using superiority and inferiority measures , 2011, Stochastic Environmental Research and Risk Assessment.

[39]  J. Birge,et al.  A multicut algorithm for two-stage stochastic linear programs , 1988 .

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

[41]  Arturo A. Keller,et al.  Uncertainty assessment in watershed‐scale water quality modeling and management: 1. Framework and application of generalized likelihood uncertainty estimation (GLUE) approach , 2007 .

[42]  Koichi Unami,et al.  Fuzzy optimization model for integrated management of total nitrogen loads from distributed point and nonpoint sources in watershed , 2009, Paddy and Water Environment.

[43]  Donald J. O'Connor,et al.  Mechanism of Reaeration in Natural Streams , 1958 .

[44]  S. M. Shahidehpour,et al.  A dynamic programming two-stage algorithm for long-term hydrothermal scheduling of multireservoir systems , 1998 .

[45]  Guo H. Huang,et al.  An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty , 2007, Eur. J. Oper. Res..

[46]  Guohe Huang,et al.  A GREY LINEAR PROGRAMMING APPROACH FOR MUNICIPAL SOLID WASTE MANAGEMENT PLANNING UNDER UNCERTAINTY , 1992 .