IFMP: Interval-fuzzy multistage programming for water resources management under uncertainty

An interval-fuzzy multistage programming (IFMP) method is developed for water resources management under uncertainty. This method improves upon the existing multistage stochastic programming methods by allowing uncertainties presented as discrete intervals, fuzzy sets, and probability distributions to be effectively incorporated within its optimization framework. The IFMP method can adequately reflect dynamic variations of system conditions, particularly for large-scale multistage problems with sequential structures. The uncertain information can be incorporated within a multi-layer scenario tree; revised decisions are permitted in each time period based on the realized values of the uncertain events. Moreover, this method can be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. A case study of water resources management is then provided for demonstrating applicability of the developed method. For all scenarios under consideration, corrective actions are allowed to be taken dynamically in reference to the pre-regulated policies and the realized uncertainties. The results can help quantify the relationships among system benefit, satisfaction degree, and constraint-violation risk. Thus, desired decision alternatives can be generated under different conditions of supply-demand dynamics.

[1]  John R. Birge,et al.  Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs , 1985, Oper. Res..

[2]  Roman Słowiński,et al.  An Interactive Method for Multiobjective Linear Programming with Fuzzy Parameters and Its Application to Water Supply Planning , 1987 .

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

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

[5]  Janusz Kindler,et al.  Rationalizing Water Requirements with Aid of Fuzzy Allocation Model , 1992 .

[6]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[7]  Samuel O. Russell,et al.  Reservoir Operating Rules with Fuzzy Programming , 1996 .

[8]  David Maier,et al.  A Language for Spatial Data Manipulation , 2003 .

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

[10]  Guo H. Huang,et al.  An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty , 2005, Eur. J. Oper. Res..

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

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

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

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

[15]  J. Kacprzyk,et al.  Optimization Models Using Fuzzy Sets and Possibility Theory , 1987 .

[16]  G. H. Huang,et al.  An Interval-Parameter Fuzzy-Stochastic Programming Approach for Municipal Solid Waste Management and Planning , 2001 .

[17]  M. V. F. Pereira,et al.  Multi-stage stochastic optimization applied to energy planning , 1991, Math. Program..

[18]  Ni-Bin Chang,et al.  A fuzzy interval multiobjective mixed integer programming approach for the optimal planning of solid waste management systems , 1997, Fuzzy Sets Syst..

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

[20]  Julian Scott Yeomans,et al.  An Evolutionary Grey, Hop, Skip, and Jump Approach: Generating Alternative Policies for the Expansion of Waste Management , 2003 .

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

[22]  Jitka Dupacová,et al.  Scenarios for Multistage Stochastic Programs , 2000, Ann. Oper. Res..

[23]  S Vedula,et al.  Multireservoir System Optimization using Fuzzy Mathematical Programming , 2000 .

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

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

[26]  Ni-Bin Chang,et al.  A grey fuzzy multiobjective programming approach for the optimal planning of a reservoir watershed. Part A: Theoretical development , 1996 .

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

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

[29]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

[30]  Keith W. Hipel,et al.  Water Resources Allocation: A Cooperative Game Theoretic Approach , 2003 .

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

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

[33]  D. Dubois,et al.  Systems of linear fuzzy constraints , 1980 .

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

[35]  Andrzej Ruszczynski,et al.  Parallel decomposition of multistage stochastic programming problems , 1993, Math. Program..