A Multiobjective Fuzzy Stochastic Program For Water Resources Optimization: The Case Of Lake Management

Abstract In many real decision situations more than one objective has to be considered and different kinds of uncertainty must be handled. The uncertainty is generally of two natures: stochastic uncertainly related to environmental data and fuzzy uncertainty related to expert judgement. This paper proposes a fuzzy chance constrained approach to solve mathematical programs integrating fuzzy and stochastic parameters with multiple objective aspects. Our approach is applied to determine reservoirs releases in the Echkeul basin in Tunisia.

[1]  M. K. Luhandjula.  Linear programming under randomness and fuzziness , 1983 .

[2]  M. Houck.  A Chance Constrained Optimization Model for reservoir design and operation , 1979 .

[3]  C. Revelle,et al.  The Linear Decision Rule in Reservoir Management and Design: 1, Development of the Stochastic Model , 1969 .

[4]  Raymond Nadeau,et al.  Multiobjective Stochastic Linear Programming with Incomplete Information: A General Methodology , 1990 .

[5]  Lucien Duckstein,et al.  Regional management of an aquifer for mining under fuzzy environmental objectives , 1983 .

[6]  George B. Dantzig,et al.  Linear Programming Under Uncertainty , 2004, Manag. Sci..

[7]  신항식,et al.  Application of Fuzzy Sets to Water Quality Management , 1985 .

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

[9]  W. Mohammed.  Chance constrained fuzzy goal programming with right-hand side uniform random variable coefficients , 2000, Fuzzy Sets Syst..

[10]  Yaguang Yang.  A new approach to uncertain parameter linear programming , 1991 .

[11]  M. P. Biswal,et al.  Fuzzy programming approach to multi-objective stochastic programming problems when bi's follow joint normal distribution , 2000, Fuzzy Sets Syst..

[12]  Benoît Julien,et al.  Water quality management with imprecise information , 1994 .

[13]  Bithin Datta,et al.  Short-Term, Single, Multiple-Purpose Reservoir Operation: Importance of Loss Functions and Forecast Errors , 1984 .

[14]  Ben Abdelaziz Foued,et al.  Application of goal programming in a multi-objective reservoir operation model in Tunisia , 2001, Eur. J. Oper. Res..

[15]  Baoding Liu,et al.  A note on chance constrained programming with fuzzy coefficients , 1998, Fuzzy Sets Syst..

[16]  Ichiro Nishizaki,et al.  An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model , 2003, Eur. J. Oper. Res..

[17]  Baoding Liu,et al.  Dependent-chance programming in fuzzy environments , 2000, Fuzzy Sets Syst..

[18]  C. Hwang,et al.  Fuzzy Multiple Objective Decision Making: Methods And Applications , 1996 .

[19]  Ambrose Goicoechea,et al.  Multiple objectives under uncertainty: An illustrative application of protrade , 1979 .

[20]  P. W. Jowitt.  Fuzzy Sets and Water Quality , 1984 .