Inexact joint-probabilistic stochastic programming for water resources management under uncertainty

References

• Abbaspour , M. and Nobakhti , H. 2009 . 3D model for evaluation of pollutant concentration distributions from land-based sources of the Caspian Sea region - regional study, southern part of the Caspian Sea . Journal of Environmental Informatics , 14 ( 1 ) : 51 – 65 .
   Google Scholar
• Ahmed , S. , Tawarmalani , M. and Sahinidis , N. V. 2004 . A finite branch-and-bound algorithm for two-stage stochastic integer programs . Mathematic Program Search A , 100 : 355 – 377 .
   Web of Science ®Google Scholar
• Bashir , M. A. , Tanakamaru , H. and Tada , A. 2009 . Spatial and temporal analysis of evapotranspiration using satellitie remote sensing data: a case study in the Gezira Scheme, Sudan . Journal of Environmental Informatics , 13 ( 2 ) : 86 – 92 .
   Google Scholar
• Beale , E. 1955 . On minimizing a convex function subject to linear inequalities . Journal of the Royal Statistical Society B , 17 : 173 – 184 .
   Google Scholar
• Billiomet , A. 2009 . Estimation of spatial influence models using mixed-integer programming . Journal of Environmental Informatics , 14 ( 1 ) : 31 – 40 .
   Google Scholar
• Birge , J. R. and Louveaux , F. V. 1988 . A multicut algorithm for two-stage stochastic linear programs . European Journal of Operational Research , 34 : 384 – 392 .
   Web of Science ®Google Scholar
• Birge , J. R. and Louveaux , F. V. 1997 . Introduction to stochastic programming , New York : Springer .
   Google Scholar
• Charnes , A. , Cooper , W. W. and Kirby , P. 1972 . “ Chance constrained programming: An extension of statistical method ” . In Optimizing methods in statistics , 391 – 402 . New York : Academic Press .
   Google Scholar
• Charnes , A. and Cooper , W. W. 1983 . Response to decision problems under risk and chance constrained programming: Dilemmas in the transitions . Management Science , 29 : 750 – 753 .
   Web of Science ®Google Scholar
• Dantzig , G. B. 1983 . “ Reminiscences about the origins of linear programming ” . In Mathematical programming: The state of the art , Edited by: Bachem , A. , Grötschel , M. and Korte , B. Berlin : Springer-Verlag .
   Google Scholar
• Dupačová , J. , Gaivoronski , A. , Kos , Z. and Szantai , T. 1991 . Stochastic programming in water management: A case study and a comparison of solution techniques . European Journal of Operational Research , 52 : 28 – 44 .
   Web of Science ®Google Scholar
• Ellis , J. H. 1991 . Stochastic programs for identifying critical structural collapse mechanisms . Applied Mathematical Modelling , 15 : 367 – 379 .
   Web of Science ®Google Scholar
• Edirisinghe , N. C.P. , Patterson , E. I. and Saadouli , N. 2000 . Capacity planning model for a multipurpose water reservoir with target-priority operation . Annals of Operations Research , 100 : 273 – 303 .
   Google Scholar
• Ferrero , R. W. , Rivera , J. F. and Shahidehpour , S. M. 1998 . A dynamic programming two-stage algorithm for long-term hydrothermal scheduling of multireservoir systems . IEEE – Transactions on Power Systems , 13 : 1534 – 1540 .
   Web of Science ®Google Scholar
• Fujiwara , O. , Puangmaha , W. and Hanaki , K. 1988 . River basin quality management in stochastic environment . ASCE – Journal of Environmental Engineering , 114 : 864 – 880 .
   Web of Science ®Google Scholar
• Huang , G. H. , Baetz , B. W. and Patry , G. G. 1995 . Grey integer programming: An application to waste management planning under uncertainty . European Journal of Operational Research , 83 : 594 – 620 .
   Web of Science ®Google Scholar
• Huang , G. H. 1998 . A hybrid inexact-stochastic water management model . European Journal of Operational Research , 107 : 137 – 158 .
   Web of Science ®Google Scholar
• Huang , G. H. and Loucks , D. P. 2000 . An inexact two-stage stochastic programming model for water resources management under uncertainty . Civil Engineering and Environmental Systems , 17 : 95 – 118 .
   Web of Science ®Google Scholar
• Infanger , G. 1993 . Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs . Annals of Operations Research , 39 : 69 – 81 .
   Google Scholar
• Iskenderov , A. A. 2003 . A mathematical model of water supply system management . Water Resources , 30 ( 4 ) : 458 – 466 .
   Google Scholar
• Lejeune , M. A. and Prekopa , A. 2005 . Approximations for and convexity of probabilistic constrained problems with random right-hand sides . RRR – Rutcor Research Report , 17 : 1 – 5 .
   Google Scholar
• Li , Y. P. , Huang , G. H. and Nie , S. L. 2006 . An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty . Advances in Water Resources , 29 : 776 – 789 .
   Web of Science ®Google Scholar
• Li , Y. P. , Huang , G. H. and Nie , S. L. 2007a . Mixed interval-fuzzy two-stage integer programming and its application to flood-diversion planning . Engineering Optimization , 39 ( 2 ) : 163 – 183 .
   Web of Science ®Google Scholar
• Li , Y. P. , Huang , G. H. , Nie , S. L. and Qin , X. S. 2007b . ITCLP: An inexact two-stage chance-constrained program for planning waste management systems . Resources, Conservation and Recycling , 49 ( 3 ) : 284 – 307 .
   Web of Science ®Google Scholar
• Li , Y. P. and Huang , G. H. 2008 . Interval-parameter two-stage stochastic nonlinear programming for water resources management under uncertainty . Water Resources Management , 22 : 681 – 698 .
   Google Scholar
• Li , Y. P. , Huang , G. H. , Nie , S. L. and Mo , D. W. 2008 . Interval-parameter robust quadratic programming for water quality management under uncertainty . Engineering Optimization , 40 ( 7 ) : 613 – 635 .
   Web of Science ®Google Scholar
• Liu , Z. F. , Huang , G. H. , Liao , R. F. and He , L. 2009 . DIPIP: Dual Interval Probabilistic Integer Programming for solid waste management . Journal of Environmental Informatics , 14 ( 1 ) : 66 – 73 .
   Google Scholar
• Lohani , B. N. and Hee , K. B. 1983 . A CCDP model for water quality management in the Hsintien river in Taiwan . International Journal of Water Resources Development , 1 ( 2 ) : 91 – 114 .
   Google Scholar
• Loucks , D. P. , Stedinger , J. R. and Haith , D. A. 1981 . Water resource systems planning and analysis , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Maqsood , I. , Huang , G. H. and Yeomans , J. S. 2005 . An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty . European Journal of Operational Research , 167 : 208 – 225 .
   Web of Science ®Google Scholar
• Miller , B. L. and Wager , H. M. 1965 . Chance constrained programming with joint constraints . Operations Research , 13 ( 6 ) : 930 – 945 .
   Web of Science ®Google Scholar
• Morgan , D. R. , Eheart , J. W. and Valocchi , A. J. 1993 . Aquifer remediation design under uncertainty using a new chance constrained programming technique . Water Resources Research , 29 : 551 – 568 .
   Web of Science ®Google Scholar
• Pereira , M. V.F. and Pinto , L. M.V.G. 1985 . Stochastic optimization of a multireservior hydroelectric system: a decomposition approach . Water Resources Research , 6 : 779 – 792 .
   Web of Science ®Google Scholar
• Rangarajan , S. 1995 . Sustainable planning of the operation of reservoirs for hydropower generation , Winnipeg, , Canada : University of Manitoba . Thesis (PhD), Department of Civil Engineering
   Google Scholar
• ReVelle , C. 1999 . Optimizing reservoir resources: Including a new model for reservoir reliability , New York : John Wiley & Sons, Inc .
   Google Scholar
• Seifi , A. and Hipel , K. W. 2001 . Interior-point method for reservoir operation with stochastic inflows . Journal of Water Resources Planning and Management , 127 ( 1 ) : 48 – 57 .
   Web of Science ®Google Scholar
• Srinivasan , R. and Simonovic , S. P. 1994 . A reliability programming model for hydropower optimization . Canadian Journal of Civil Engineering , 21 : 1061 – 1073 .
   Google Scholar
• Zhang , Y. , Monder , D. and Forbes , J. F. 2002 . Real-time optimization under parametric uncertainty: a probability constrained approach . Journal of Process Control , 12 : 373 – 389 .
   Web of Science ®Google Scholar